  The paper discusses a holomorphic nonlinear singular partial differential
equation $(t \partial_t)^mu=F(t,x,\{(t \partial_t)^j
  \partial_x^{\alpha}u \}_{j+\alpha \leq m, j<m})$ under the assumption that
the equation is of nonlinear totally characteristic type. By using the Newton
Polygon at $x=0$, the notion of the irregularity at $x=0$ of the equation is
defined. In the case where the irregularity is greater than one, it is proved
that every formal power series solution belongs to a suitable formal Gevrey
class. The precise bound of the order of the formal Gevrey class is given, and
the optimality of this bound is also proved in a generic case.
