  A system of a metastable phase with several sorts of heterogeneous centers is
considered. An analytical theory for the process of decay in such a system has
been constructed. The free energy of formation of a critical embryo is assumed
to be known in the macroscopic approach. At first all asymptotic cases are
investigated and then a general intermediate solution is suggested. All
approximate transformations are accomplished with the corresponding numerical
estimates and analytical justifications. This is the first part of the
manuscript, the second part is cond-mat/0210619 .
