  The method which allows for asymptotic expansion of the one-loop effective
action W=ln det A is formulated. The positively defined elliptic operator A= U
+ M^2 depends on the external classical fields taking values in the Lie algebra
of the internal symmetry group G. Unlike the standard method of Schwinger -
DeWitt, the more general case with the nondegenerate mass matrix
M=diag(m1,m2,...) is considered. The first coefficients of the new asymptotic
series are calculated and their relationship with the Seeley-DeWitt
coefficients is clarified.
