  The present paper deals with sufficient conditions for orbital stability of
periodic waves of a general class of evolution equations supporting nonlinear
dispersive waves. Our method can be seen as an extension to spatially periodic
waves of the theory of solitary waves recently developed in \cite{st}. Firstly,
our main result do not depend on the parametrization of the periodic wave
itself. Secondly, motived by the well known orbital stability criterion for
solitary waves, we show that the same criterion holds for periodic waves. In
addition, we show that the positiveness of the principal entries of the Hessian
matrix related to the "energy surface function" are also sufficient to obtain
the stability. Consequently, we can establish the orbital stability of periodic
waves for several nonlinear dispersive models. We believe our method can be
applied in a wide class of evolution equations; in particular it can be
extended to regularized dispersive wave equations.
