  The branching fractions for the inclusive Cabibbo-favored ~K*0 and
Cabibbo-suppressed K*0 decays of D mesons are measured based on a data sample
of 33 pb-1 collected at and around the center-of-mass energy of 3.773 GeV with
the BES-II detector at the BEPC collider. The branching fractions for the
decays D+(0) -> ~K*0(892)X and D0 -> K*0(892)X are determined to be BF(D0 ->
\~K*0X) = (8.7 +/- 4.0 +/- 1.2)%, BF(D+ -> ~K*0X) = (23.2 +/- 4.5 +/- 3.0)% and
BF(D0 -> K*0X) = (2.8 +/- 1.2 +/- 0.4)%. An upper limit on the branching
fraction at 90% C.L. for the decay D+ -> K*0(892)X is set to be BF(D+ -> K*0X)
< 6.6%.
