The method which allows for asymptotic expansion of the one‐loop effective actionW= lndetAis formulated. The positively defined elliptic operatorA = U+M2depends on the external classical fields taking values in the Lie algebra of the internal symmetry groupG. Unlike the standard method of Schwinger ‐ DeWitt, the more general case with the nongenerate mass matrixM= diag(m1,m2, &ellip;) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley ‐ DeWitt coefficients is clarified. © 2003 American Institute of Physics