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Higher-order process calculi, for its abstraction capability and theoretical significance, have constantly been receiving much attention in the field of process calculi, and stand as a mathematical tool for describing and analyzing mobile systems with dynamically changing inter-connection structures. In this thesis we contribute to the higher-order paradigm in several aspects. • Higher-order π-calculus with mismatch: the bisimulation theory. Linear fragment of higherorder π-calculus with mismatch: the axiomatization. The problem of the axiomatization of higher-order process calculi, such as higher-order πcalculus, is always a non-trivial one. However, it is important, both in theory and practice, to be able to decide whether two higher-order processes are equivalent with respect to some bisimulation, which needs an algorithm that can effectively analyze and give an answer efficiently. We further the available work by considering the higher-order π-calculus with mismatch, which is a useful operator in bisimulation theory and especially the axiomatization, from algorithmic point of view. We first formulate the bisimulation theory, where the bisimulation we define is called open weak higher-order bisimulation, which is a non-delayed