David Ambrose Drexel University For the mean field games system, in practice, non-separable Hamiltonians are frequently of interest. We discuss existence proofs for strong solutions in the case of non-separable Hamiltonians. The functional settings considered include spaces based on the Wiener algebra, and also standard Sobolev spaces. Our various results all require a smallness constraint, and this can be on the size of the data, on the size of the time interval, or on the Hamiltonian itself.