  Let ${mathcal M}_g^n$ be the moduli space of n-pointed Riemann surfaces of
genus g. Denote by ${\bar {\mathcal M}}_g^n$ the Deligne-Mumford
compactification of ${mathcal M}_g^n$. In the present paper, we calculate the
orbifold and the ordinary Euler characteristic of ${\bar {\mathcal M}}_g^n$ for
any g and n such that n>2-2g.
