  Spin networks are natural generalization of Wilson loops functionals. They
have been extensively studied in the case where the gauge group is compact and
it has been shown that they naturally form a basis of gauge invariant
observables. Physically the restriction to compact gauge group is enough for
the study of Yang-mills theories, however it is well known that non-compact
groups naturally arise as internal gauge groups for Lorentzian gravity models.
In this context a proper construction of gauge invariant observables is needed.
The purpose of this work is to define the notion of spin network states for
non-compact groups. We first built, by a careful gauge fixing procedure, a
natural measure and a Hilbert space structure on the space of gauge invariant
graph connection. Spin networks are then defined as generalized eigenvectors of
a complete set of hermitic commuting operators. We show how the delicate issue
of taking the quotient of a space by non compact groups can be address in term
of algebraic geometry. We finally construct the full Hilbert space containing
all spin network states. Having in mind application to gravity we illustrate
our results for the groups SL(2,R), SL(2,C).
