  We analyze asymptotic convergence properties of Newton's method for a class
of evolutive Mean Field Games systems with non-separable Hamiltonian arising in
mean field type models with congestion. We prove the well posedness of the Mean
Field Game system with non-separable Hamiltonian and of the linear system
giving the Newton iterations. Then, by forward induction and assuming that the
initial guess is sufficiently close to the solution of problem, we show a
quadratic rate of convergence for the approximation of the Mean Field Game
system by Newton's method. We also consider the case of a nonlocal coupling,
but with separable Hamiltonian, and we show a similar rate of convergence.
