In this paper, we initiate the investigation of two parameter C0 and C−groups of bounded linear operators on non-Archimedean Banach spaces. In contrast with the classical setting, the two-parameter of a given C0 or C−group belongs to a clopen ball Ω 2 r of the ground non-Archimedean field K 2. We check some properties of two parameter C−groups of linear operators on non-Archimedean Banach spaces and we give some examples to support our work.