  A multivariate, formal power series over a field $K$ is a B\'ezivin series if
all of its coefficients can be expressed as a sum of at most $r$ elements from
a finitely generated subgroup $G \le K^*$; it is a P\'olya series if one can
take $r=1$. We give explicit structural descriptions of $D$-finite B\'ezivin
series and $D$-finite P\'olya series over fields of characteristic $0$, thus
extending classical results of P\'olya and B\'ezivin to the multivariate
setting.
