Branches of foreign banks are allowed, but foreign participation in local banks is limited to 60% by SAMA regulations. 
[text not available] (Rules of Acquisition and Disposal of Ownership of Banks, SAMA Banking Policy Department)
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"16. [...] Foreign banks may operate in Saudi Arabia either as locally incorporated joint-stock companies or as branches of international banks. Non-Saudi participation in a joint venture is permitted up to 60%.
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4.5. The banks and insurance sector are regulated by the Saudi Arabia Monetary Agency (SAMA) and capital markets are regulated by the Capital Markets Authority (CMA). There are 12 commercially licensed domestic banks and 12 licensed commercial bank branches of foreign banks operating in Saudi Arabia. To get a banking licence, a natural or legal person must be a Saudi national or a joint venture with a public Saudi joint-stock company and meet prudential criteria.
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4.82. The main legislation governing the banking sector continues to be the Banking Control Law of 1966, which is administered by SAMA.44 Under the provisions of the Law and the Charter of SAMA, SAMA is responsible for inter alia: developing and administering the regulatory and supervisory framework, including issuing guidelines pertaining to supervision, operations and inspections; issuing licences; and onsite and offsite inspection. Under Article 2 of the Banking Control Law, a natural or legal person is required to have a licence to engage in a banking business. Under Article 3 of the Law, the licensing requirements for a Saudi national bank or a joint venture bank stipulate that it must be a public Saudi joint-stock company.
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4.83. Foreign banks are allowed to operate in Saudi Arabia either as a locally incorporated jointstock company or as a branch of an international bank. Non-Saudi participation in a joint venture is permitted up to 60%. [...]" (WTO (2016), Trade Policy Review of the Kingdom of Saudi Arabia, WT/TPR/S/333 29 February 2016)
Rules of Acquisition and Disposal of Ownership of Banks, SAMA Banking Policy Department
[<a href="n/a">Rules</a>],[<a href="https://www.wto.org/english/tratop_e/tpr_e/s333_e.pdf">Other</a>]