The initial value problems for field equations (in mechanics, equations of motion) with higher derivative or non-local couplings are investigated on the basis of the perturbation theory. Especially it is the purpose of this paper to clarify how all higher derivatives of dynamical variables may be deduced from the prescribed initial values of the same degrees of freedom as those of free equations. The propagation character of those fields are also investigated, applying the characteristic theory

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... of hyperbolic differential equations. * In this paper, the coupling constants are always assumed to be sufficiently small and all quantities are c-number unless there is some particular note given.