Let pi be an automorphic representation of GSp(4) with an associated
compatible family of p-adic Galois representations.

We consider the deformations of the resulting residual representations. We show that, under appropriate hypotheses, the local obstructions to these deformation problems vanish for almost all primes p. Combined with relevant Taylor-Wiles style results as in the work of Genestier-Tilouine), this shows that the universal deformation ring is usually a power series ring.