  Non-Markovian stochastic Langevin-like equations of motion are compared to
their corresponding Markovian (local) approximations. The validity of the local
approximation for these equations, when contrasted with the fully nonlocal
ones, is analyzed in details. The conditions for when the equation in a local
form can be considered a good approximation are then explicitly specified. We
study both the cases of additive and multiplicative noises, including system
dependent dissipation terms, according to the Fluctuation-Dissipation theorem.
