The analytic and numerical solution of the 1$frac{1}{2}$-layer and 2$frac{1}{2}$-layer models are derived. The large coastal-sea level drop and the fast westward speed of the anticyclonic gyre due to strong offshore winds using two ocean models are investigated. The models are forced by wind stress fields similar in structure to the intense mountain-pass jets(${sim}$20 dyne/$cm^{2}$) that appear in the Gulfs of Tehuantepec and Papagayo in the Central America for periods of 3${sim}$7 days. Analytic and numerical solutions compare favorably with observations, the large sea-level drop (${sim}$30 cm) at the coast and the fast westward propagation speeds (${sim}$13 km/day) of the gyres. The coastal sea-level drop is enhanced by several factors: horizontal mixing, enhanced forcing, coastal geometry, and the existence of a second active layer in the 2$frac{1}{2}$-layer model. Horizontal mixing enhances the sea-level drop because the coastal boundary layer is actually narrower with mixing. The forcing ${ au}$/h is enhanced near the coast where h is thin. Especially, in analytic solutions to the 2$frac{1}{2}$-layer model the presence of two baroclinic modes increases the sea-level drop to some degree. Of theses factors the strengthened forcing ${ au}$/h has the largest effect on the magnitude of the drop, and when all of them are included the resulting maximum drop is -30.0 cm, close to observed values. To investigate the processes that influence the propagation speeds of anticyclonic gyre, several test wind-forced calculations were carried out. Solutions to dynamically simpler versions of the 1$frac{1}{2}$-layer model show that the speed is increased both by ${eta}$-induced self-advection and by larger h at the center ofthe gyres. Solutions to the 2$frac{1}{2}$-layer model indicate that the lower-layer flow field advects the gyre westward and southward, significantly increasing their propagation speed. The Papagayo gyre propagates westward at a speed of 12.8 km/day, close to observed speeds.