Section 139(3) of the Companies Act 71 of 2008 regulates only two scenarios: (1) in voluntary business rescue under section 129, the company retains the power to appoint a substitute practitioner upon resignation; and (2) in compulsory business rescue under section 131, the affected person who brought the application retains the power to appoint a substitute. The phrase 'or the creditor who nominated the practitioner' in section 139(3) refers to the affected person who nominated the practitioner in section 131(5), not to independent creditors contemplated in section 130(6)(a). Where a practitioner appointed by court in terms of section 130(6)(a) in place of a company-appointed practitioner resigns, the company's board has the power to appoint the replacement, subject to the right of affected persons to launch a fresh challenge under section 130(1)(b).