2-LOOP ANOMALOUS DIMENSION MATRIX FOR DELTA-S=1 WEAK NONLEPTONIC DECAYS .1. O[ALPHA(S)(2)]

We calculate the two-loop 10 x 10 anomalous dimension matrix O(alpha(s )2) involving current-current operators, QCD penguin operators, and el ectroweak penguin operators especially relevant for DELTAS = 1 weak no n-leptonic decays, but also important for DELTAB = 1 decays. The calcu lation is performed in two schemes for gamma5: the dimensional regular ization scheme with anticommuting gamma5 (NDR), and in the 't Hooft-Ve ltman scheme. We demonstrate how a direct calculation of diagrams invo lving gamma5 in closed fermion loops can be avoided thus allowing a co nsistent calculation in the NDR scheme. The compatibility of the resul ts obtained in the two schemes considered is verified and the properti es of the resulting matrices are discussed. The two-loop corrections a re found to be substantial. The two-loop anomalous dimension matrix O( alphaalpha(s)), required for a consistent inclusion of electroweak pen guin operators, is presented in a subsequent publication.