Bifurcation and perturbation techniques are used to construct small-amplitude periodic wave-trains for general systems of reaction and diffusion. All solutions are characterized by the amplitude
a
a
and the wavenumber
k
k
. For scalar diffusion,
k
∼
a
k \sim a
, while for certain types of nonscalar diffusion,
k
k
is bounded away from zero as
a
↘
0
a \searrow 0
. For certain ranges of
a
a
and
k
k
, linear stability of waves is demonstrated.