  Let $A$ be a noetherian ring and $R_A$ be the graded ring $A[X,Y,Z,T]$. In
this article we introduce the notion of a triad, which is a generalization to
families of curves in ${\bf P}^3_A$ of the notion of Rao module. A triad is a
complex of graded $R_A$-modules $(L_1 \to L_0 \to L_{-1})$ with certain
finiteness hypotheses on its cohomology modules.
  A pseudo-isomorphism between two triads is a morphism of complexes which
induces an isomorphism on the functors $ h_0 (L\otimes .)$ and a monomorphism
on the functors $h_{-1} (L\otimes .)$. One says that two triads are
pseudo-isomorphic if they are connected by a chain of pseudo-isomorphisms.
  We show that to each family of curves is associated a triad, unique up to
pseudo-isomorphism, and we show that the map $\{\hbox{families of curves}\}\to
\{\hbox{triads}\}$ has almost all the good properties of the map
$\{\hbox{curves}\}\to \{\hbox{Rao modules}\}$.
  In a section of examples, we show how to construct triads and families of
curves systematically starting from a graded module and a sub-quotient (that is
a submodule of a quotient module), and we apply these results to show the
connectedness of $H_{4,0}$.
