  Let $d,m_1,...,m_r$ be ($r+1$) positive integers, and $P_1,...,P_r$ be $r$
general points in the projective plane ; let $m$ be a positive integer. We
prove that there exists a bound $d_0(m)$ such that :
  If $m_i < m$ ($0<i<r+1$), and $d > d_0(m)$ then the linear system $L$ of
plane curves of degree $d$ having a multiplicity at least $m_i$ at each point
$P_i$ has the expected dimension ; moreover, if $L$ is not empty, there exists
an irreducible plane curve of degree $d$, smooth away from the $r$ points
$P_i$, and having an ordinary singularity of the prescribed multiplicity $m_i$
at each point $P_i$. This curve may be isolated in $L$.
