  We define a deformation space of V. Lafforgue's $G$-valued pseudocharacters
of a profinite group $\Gamma$ for a possibly disconnected reductive group $G$.
We show, that this definition generalizes Chenevier's construction. We show
that the universal pseudodeformation ring is noetherian and that the functor of
continuous $G$-pseudocharacters on affinoid $\mathbb{Q}_p$-algebras is
represented by a quasi-Stein rigid analytic space, whenever $\Gamma$ is
topologically finitely generated. We also show that the pseudodeformation ring
is noetherian, when $\Gamma$ satisfies Mazur's condition $\Phi_p$ and $G$
satisfies a certain invariant-theoretic condition. For $G = \mathrm{Sp}_{2n}$
we describe three types of obstructed loci in the special fiber of the
universal pseudodeformation space of an arbitrary residual pseudocharacter and
give upper bounds for their dimension.
