Part 1 of this study is a descriptive analysis of the spreading of Mediterranean Water based on high-resolution maps of salinity and density in the eastern basin. In this second part of our study, velocity fields for two representative isopycnal surfaces of the Mediterranean outflow (&sgr;0.5=29.70 and &sgr;0.5=29.90) are estimated from a diagnostic model that combines climatological hydrographic data from the National Oceanic Data Center with long-term direct measurements of water exchange through the Strait of Gibraltar. The model is constrained by geostrophic dynamics, conservation of mass, no-flux conditions at the continental shelf, and specified flow through the Strait of Gibraltar. Our principal data source is a recently assembled database of the North Atlantic that consists of climatological mean property fields averaged on isopycnal surfaces. The mean fields are based on more than 80 years (1909--1990) of data and have a nominal horizontal resolution of 0.5¿. To provide boundary conditions at the Strait of Gibraltar, we use the results of a model developed from data collected during the Gibraltar Experiment in 1985. The estimated velocity fields show Mediterranean Water exiting the Strait of Gibraltar, following the southern Iberian coast, and then entering the Tagus Basin, where it turns anticyclonically to create a reservoir of this water mass. The flow continues northward along the eastern boundary, penetrating into the Rockall Channel. Finally, the model flow fields do not show a significant westward advection of Mediterranean waters into the subtropical gyre. ¿ 1999 American Geophysical Union