Calculation of superpropagators in non-linear quantum field theories

A new method of constructing the superpropagators, i.e. the Fourier transforms of the expressions of the form is suggested. The method makes it possible to derive by use of the same technique explicit analytic expressions for the superpropagators for a wide class of field theories — from strictly local up to essentially non-local. The essence of the method is the construction of a differential equation for the superpropagator which in general is of an infinite order. By use of the boundary condition atp²=0 we find the solution of this equation depending on one arbitrary real parameter. Simple examples are given to illustrate the method.