  Let $A$ be a local noetherian ring and $N$ be a locally sheaf on the
projective space $P^3_A$ : one proves easily that there exists a family $C$ of
(smooth connected) curves contained in $P^3_A$, flat over $A$, and an integer
$h$ such that the ideal sheaf $J$ of $C$ has a resolution $0\to P\to N\to J\to
0$ where $P$ is a direct sum of invertible sheaves $O_P(-n_i)$. In this paper
we determine, for a given sheaf $N$, all the families of curves with such a
resolution, especially the minimal ones (corresponding to the minimum value of
$h$). It gives a description of the biliaison class related to $N$, and a tool
for constructing families of space curves.
