  The paper deals with path-dependent Hamilton-Jacobi equations with a
coinvariant derivative which arise in investigations of optimal control
problems and differential games for neutral-type systems in Hale's form. A
viscosity (generalized) solution of a Cauchy problem for such equations is
considered. The existence, uniqueness, and consistency of the viscosity
solution are proved. Equivalent definitions of the viscosity solution,
including the definitions of minimax and Dini solutions, are obtained.
Application of the results to an optimal control problem for neutral-type
systems in Hale's form are given.
