The paper deals with a non-linear singular partial differential equation
(E) t partial derivative/partial derivativet = F(t,x, u, partial derivative
u/partial derivativex)
in the holomorphic category. When (E) is of Fuchsian type, the existence of
the unique holomorphic solution was established by GERARD - TAHARA [2]. In
this pager, under the assumption that (E) is of totally characteristic typ
e, the authors give a sufficient condition for (E) to have a unique holomor
phic solution. The result is extended to higher order case.