In this article we describe a new method to construct fundamental solutions for operators with variable coefficients. That method was introduced in {\it J. Differential Equations} {\bf 206} (2004), 227-252, to study the Tricomi-type equation. More precisely, the new integral operator is suggested which transforms the family of the fundamental solutions of the Cauchy problem for the equation with the constant coefficients to the fundamental solutions for the operators with variable coefficients.
