The author explains his ideas in order to obtain generalized modular functions of several variables. It is expected that, if one has a good family of K3-surfaces over a parameter \(space\quad T,\) one can proceed similarly as in the classical case of elliptic curves. For example, the periods are to satisfy differential equations of hyper-geometric type, the period mapping is to be a mapping into a domain D with \(\dim (D)=\dim (T)\), and the inverse of it is to be expressed explicitly by automorphic functions and forms on D with respect to the monodromy action. The author exhibits several examples of such families to which his method applies. Every K3-surface in these examples admits an elliptic fibration with a holomorphic section. Proofs are found in the author’s other papers.