  In this paper, we study a class of first order nonlinear degenerated partial
differential equations with singularity at $(t,x)=(0,0)\in \CC^2$. By means of
exponential type Nagumo norm approach, Gevrey asymptotic analysis extends to
case of holomorphic parameters by a natural way. A sharp condition is then
established to deduce the $k$-summability for the formal solutions.
Furthermore, analytical solutions in conical domains are found for each type of
these nonlinear singular PDEs.
