  We establish the existence of small-amplitude uni- and bimodal steady
periodic gravity waves with an affine vorticity distribution, using a
bifurcation argument that differs slightly from earlier theory. The solutions
describe waves with critical layers and an arbitrary number of crests and
troughs in each minimal period. An important part of the analysis is a fairly
complete description of the local geometry of the so-called kernel equation,
and of the small-amplitude solutions. Finally, we investigate the asymptotic
behavior of the bifurcating solutions.
