AbstractRegarding behaviour equivalence in higher-order process calculi, Sangiorgi (Inform. and Comput. 131 (1996) 141) and Thomsen (Inform. and Comput. 116 (1995) 38) introduced context and higher-order bisimulations, respectively. In this paper, uniqueness of solutions of equations with respect to strong context and higher-order bisimilarities and compatibility of strong context and higher-order bisimilarities with recursive definitions are shown