  The direct electron spin resonance (ESR) absorption between a singlet ground
state and the triplet excited states of spin gap systems is investigated. Such
an absorption, which is forbidden by the conservation of the total spin quantum
number in isotropic Hamiltonians, is allowed by the Dzyaloshinskii-Moriya
interaction. We show a selection rule in the presence of this interaction,
using the exact numerical diagonalization of the finite cluster of the
quasi-one-dimensional bond-alternating spin system. The selection rule is also
modified into a suitable form in order to interpret recent experimental results
on CuGeO$_3$ and NaV$_2$O$_5$.
