LetD1,D2,…Dmbe anympartial derivative operators inwith the formwherej= (j1,j2,…jn) is a multi-index. Suppose thatfis an entire function inthat is a solution of the partial functional-differential equationF(D1y,D2y,…Dmy)= 0, whereFis an entire function inor more generally, a formal power series inD1y,D2y,…Dmywith coefficients being small functions offWe give in this paper a reduction theorem which shown whenfa solution of a much simpler equationP(D1y,D2y,…Dmy= 0, wherePis a non-zero polynomial inD1y,D2y,…Dmy.