Investigation is made into the response of an equatorial ocean to growing and moving zonal wind systems as motivated by observations of maximum upwelling central to the equatorial Atlantic basin and westward progressing thermal and momentum signatures near the surface. Analytical solutions to the linear, reduced gravity, equatorial β-plane equations of motion subject to a long wave approximation are given for three easterly forcing functions: 1) linearly expanding fetch with constant stress, 2) linearly expanding fetch and stress, and 3) constant fetch and stress, translating westward. The results, as they may relate to the equatorial Atlantic Ocean, are discussed.