  The asymptotic behavior of a family of singularly perturbed PDEs in two time
variables in the complex domain is studied. The appearance of a multilevel
Gevrey asymptotics phenomenon in the perturbation parameter is observed. We
construct a family of analytic sectorial solutions in $\epsilon$ which share a
common asymptotic expansion at the origin, in different Gevrey levels. Such
orders are produced by the action of the two independent time variables.
