  We present the numbers of dimer-monomers on the Sierpinski gasket $SG_d(n)$
at stage $n$ with dimension $d$ equal to two, three and four, and determine the
asymptotic behaviors. The corresponding results on the generalized Sierpinski
gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4$ are obtained.
