The nonlinear nature of the in situ density of seawater as a function of the potential temperature, pressure and salinity causes two vertical advection processes (thermobaricity and cabbeling) and also complicates the use of microstructure data to deduce upwelling velocities. Cabbeling and thermobaricity are evaluated and mapped on some neutral surfaces in each of the world's oceans by taking the lateral flux of scalars to be parameterized by a lateral diffusivity. In most of the ocean, these two processes are weak, but where there is a significant epineutral gradient of potential temperature, the downwelling due to cabbeling is quite large. In the Southern ocean, where there is a large slope of the neutral surfaces, thermobaricity causes a larger downwelling velocity than cabbeling, and the two processes together cause a dianeutral velocity of about -2¿10-7 m s-1. The complementary roles of vertical mixing and vertical advection in achieving water-mass conversion are demonstrated, since maps of the dineutral motion caused by vertical mixing are quite different to maps of water-mass conversion caused by the same process. This emphasizes the need to include both vertical advection and vertical mixing in ocean models. The method that is used to infer the upwelling velocity from microstructure dissipation measurements is also significantly affected by the nonlinear nature of the equation of state. The extra term that needs to be included in this method is a strong function of depth, changing sign at a depth of about 1500 m. ¿ American Geophysical Union 1990