From 1999 onwards, no more restrictions apply with regard to foreign shareholding in Australian carriers operating domestic services, unless this is contrary to the national interest and with the exception of Qantas. Before that, foreign airlines flying to Australia could only expect approval to acquire up to 25% of the equity in a carrier operating domestic services individually or up to 40% in aggregate provided the proposal was not contrary to the national interest. 
Since 2000, foreign participation in locally incorporated air carriers operating international traffic ("Australian international airlines") has been limited to 49%. Previously, ownership by foreign airlines was limited to 35% of the share capital in aggregate, and individual holdings by foreign airlines were limited to 25%. In 2000, the legislation was amended and the ownership limit by foreign persons (including but not limited to foreign airlines) was increased to 49% in aggregate, and the separate limit for individual holdings was lifted.
In addition, a special regime limits foreign ownership in Qantas, a privately owned flag carrier, to 49%. Prior to 2014, in addition to the general 49% foreign equity limitation, the Qantas Sales Act 1992 limited foreign individual equity holdings in Quantas to 25% and aggregate ownership by foreign airlines to 35%. 
"11A Foreign shareholdings in Australian international airlines
 (1) The Minister may, by written notice, require an Australian international airline:
 (a) to give to the Minister such information as is specified in the notice concerning the extent (if any) to which foreign persons have relevant interests in shares in the Australian international airline; or
 (b) if foreign persons have relevant interests in shares in the Australian international airline that represent, in total, more than 49% of the total value of the issued share capital of the Australian international airline—to take all necessary action to ensure that its constitution complies with subsection (2).
 (2) The constitution of an Australian international airline complies with this subsection if it:
 (a) imposes restrictions on the issue and ownership (including joint ownership) of shares in the Australian international airline so as to prevent foreign persons having relevant interests in shares in the Australian international airline that represent, in total, more than 49% of the total value of the issued share capital of the Australian international airline; and
 (c) confers the following powers on the directors of the Australian international airline to enable the directors to enforce the restrictions referred to in paragraph (a):
 (i) the power to do anything necessary to effect the transfer of shares held by a person;
 (ii) the power to remove or limit the right of a person to exercise voting rights attached to voting shares;
 (iii) the power to end the appointment of a person to the office of director of the Australian international airline.
 (3) For the purposes of this section, a person has a relevant interest in a share if, and only if, the person would be taken to have a relevant interest in the share for the purposes of the Corporations Act 2001 if paragraph 608(3)(a) of that Act were disregarded.
 (4) In this section:
another country includes any region:
 (a) that is part of a foreign country; or
 (b) that is under the protection of a foreign country; or
 (c) for whose international relations a foreign country is responsible.
Australian international airline means an international airline (other than Qantas) that may be permitted to carry passengers or freight, or both passengers and freight, under a bilateral arrangement as an airline designated by Australia to operate a scheduled international air service.
Australian person means:
 (a) an individual who is an Australian citizen or is ordinarily resident in Australia; or
 (b) the Commonwealth, a State or a Territory; or
 (c) a person who is a nominee of the Commonwealth or of a State or a Territory; or
 (d) a Commonwealth, State or Territory authority; or
 (e) a person who is a nominee of a Commonwealth, State or Territory authority; or
 (f) a local government body (whether incorporated or not) formed by or under a law of a State or a Territory; or
 (g) a person who is a nominee of a local government body referred to in paragraph (f); or
 (h) a body corporate that:
 (i) is incorporated by or under a law of the Commonwealth or of a State or a Territory; and
 (ii) is substantially owned and effectively controlled by persons referred to in paragraph (a), (b), (c), (d), (e), (f), (g) or (i); or
 (i) a person in the capacity of a trustee, or manager, of a fund in which the total interests (if any) of persons referred to in paragraph (a), (b), (c), (d), (e), (f), (g) or (h) represent 60% or more of the total interests in the fund.
bilateral arrangement means an agreement or arrangement between:
 (a) Australia, or an entity or organisation nominated or otherwise similarly authorised by Australia to enter into the agreement or arrangement; and
 (b) another country;
under which the carriage by air of passengers or freight (or both) is permitted.
foreign airline means an air transport enterprise other than:
 (a) an Australian international airline; or
 (b) Qantas; or
 (c) an air transport enterprise offering or operating an air service solely within Australian territory.
foreign person means:
 (a) a foreign airline; or
 (b) a person (other than a foreign airline) who is not an Australian person.
Qantas means Qantas Airways Limited, as the company exists from time to time (even if its name is later changed).
share, in relation to a body corporate, means a share in the body’s share capital.
voting share has the same meaning as in the Corporations Act 2001.[...]" (Air Navigation Act 1920 (No. 50 of 1920), last amended 21 October 2016, Section 11A)
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"7 Qantas’ articles of association to include certain provisions
 (1) The articles of association of Qantas must, on and from the day on which Qantas first becomes aware that a person, other than the Commonwealth or a nominee of the Commonwealth, has acquired voting shares in Qantas:
 (a) impose restrictions on the issue and ownership (including joint ownership) of shares in Qantas so as to prevent foreign persons having relevant interests in shares in Qantas that represent, in total, more than 49% of the total value of the issued share capital of Qantas; and  [...]
 (d) confer the following powers on the directors of Qantas to enable the directors to enforce the restrictions referred to in paragraphs (a) and (c):
 (i) the power to do anything necessary to effect the transfer of shares held by a person;
 (ii) the power to remove or limit the right of a person to exercise voting rights attached to voting shares;
 (iii) the power to end the appointment of a person to the office of director of Qantas; and  [...]
 (2) For the purposes of this section, a person has a relevant interest in a share if, and only if, the person would be taken to have a relevant interest in the share for the purposes of the Corporations Act 2001 if paragraph 608(3)(a) of that Act were disregarded.
 (3) For the purposes of this section, the question whether a person who is not an Australian citizen is ordinarily resident in Australia at a particular time is to be determined in the same manner as that question is determined under the Foreign Acquisitions and Takeovers Act 1975.
 (4) For the purposes of this section, a reference to a substantial foreign shareholding is a reference to a shareholding of 15% or more of the voting shares in Qantas in which a particular foreign person has a relevant interest.  [...]
 (7) In this section:  [...]
Australian international airline means an international airline (other than Qantas) that may be permitted to carry people or goods, or both people and goods, under a bilateral arrangement as an airline designated by Australia to operate a scheduled international air service.
Australian person means:
 (a) an individual who is an Australian citizen or is ordinarily resident in Australia; or
 (b) the Commonwealth, a State or a Territory; or
 (c) a person who is a nominee of the Commonwealth or of a State or a Territory; or
 (d) a Commonwealth, State or Territory authority; or
 (e) a person who is a nominee of a Commonwealth, State or Territory authority; or
 (f) a local government body (whether incorporated or not) formed by or under a law of a State or a Territory; or
 (g) a person who is a nominee of a local government body referred to in paragraph (f); or
 (h) a body corporate that:
 (i) is incorporated by or under a law of the Commonwealth or of a State or a Territory; and
 (ii) is substantially owned and effectively controlled by persons referred to in paragraph (a), (b), (c), (d), (e), (f), (g) or (i); or
 (i) a person in the capacity of a trustee, or manager, of a fund in which the total interests (if any) of persons referred to in paragraph (a), (b), (c), (d), (e), (f), (g) or (h) represent 60% or more of the total interests in the fund.  [...]
foreign airline means an air transport enterprise other than:
 (a) an Australian international airline; or
 (b) Qantas; or
 (c) an air transport enterprise offering or operating an air service solely within Australian territory.
foreign person means:
 (a) a foreign airline; or
 (b) a person (other than a foreign airline) who is not an Australian person. [...]" (Qantas Sale Act 1992 (No. 196 of 1992), last amended on 05 April 2018, Section 7)
Air Navigation Act 1920 (No. 50 of 1920), last amended 21 October 2016, Section 11A
Qantas Sale Act 1992 (No. 196 of 1992), last amended on 05 April 2018, Section 7
[<a href="https://www.legislation.gov.au/Details/C2016C00936">Act</a>],[<a href="https://www.legislation.gov.au/Details/C2018C00091">Act</a>]