One of the most important possibilities to represent a solution of the Vekua-equationis the factorizing-method where in w=esf—the so-called similarity-principle—the Hölder-continuous functionsturns out to be unique with the exception of a holomorphic function and wherefitself is holomorphic. By L. Bers' method to explain those solutions by virtue of a generating system, say (F,G), which involves a pseudo-holomorpliic functionw=Fφ+Gψ,φ,ψ real, one can show that even (es, ies) is such a system which will be called a main generating system. Using such systems and considering a certain extension of the path of integration one even in the theory of pseudo-holomorphic functions can deal with a theory of residues.