  We study quasilocal operators in the quantum complex sinh-Gordon theory in
the form factor approach. The free field procedure for descendant operators is
developed by introducing the algebra of screening currents and related
algebraic objects. We work out null vector equations in the space of operators.
Further we apply the proposed algebraic structures to constructing form factors
of the conserved currents $T_k$ and $\Theta_k$. We propose also form factors of
current-current operators of the form $T_kT_{-l}$. Explicit computations of the
four-particle form factors allow us to verify the recent conjecture of Smirnov
and Zamolodchikov about the structure of the exact scattering matrix of an
integrable theory perturbed by a combination of irrelevant operators. Our
calculations confirm that such perturbations of the complex sinh-Gordon model
and of the $\mathbb Z_N$ symmetric Ising models result in extra CDD factors in
the $S$ matrix.
