  In this paper, we study the Cauchy-Dirichlet problem for Parabolic complex
Monge-Amp\`ere equations on strongly pseudoconvex domains using the viscosity
method. We prove a comparison principle for Parabolic complex Monge-Amp\`ere
equations and use it to study the existence and uniqueness of viscosity
solution in certain cases where the sets $\{z\in\Omega: f(t, z)=0 \}$ may be
pairwise disjoint.
