Oceanic boundary layers (OBL) at the equator are studied using a large-eddy simulation (LES) model. The model has no equatorial undercurrent, and the vertical component of Earth's rotation is zero &OHgr;z=0. It is forced with a constant westward zonal wind stress and with a constant surface heat flux and, in some cases, a diurnal cycle of solar heating. Averaged over day 4, temperature and velocity are vertically mixed deeper for the diurnal cycling case, the surface temperature is cooler by 0.04 ¿C, and the surface velocity is weaker by 0.08 m/s, compared to a constant surface heating case with the same daily averaged surface heat flux. There is no general relationship between eddy viscosity (or diffusivity) and the gradient Richardson number, especially for the case of diurnal cycling, where nonlocal transports can lead to countergradient fluxes during nighttime convection. Sharp gradients of eddy viscosity are found near the critical Richardson number, Ri=0.25, and in the lower part of the entrainment layer where Ri≈1.0. The effect of the horizontal component of Earth's rotation &OHgr;y on an entraining equatorial OBL is also investigated. It is found in our entraining cases that with and without &OHgr;y, mean quantities (temperature, velocity) and turbulent fluxes differ no more than a few percent, in accord with the second-order closure results of Galperin et al. <1989> and Kantha et al. <1989>. The LES results are used to extend the bulk mixed layer theory of Garwood et al. <1985a, b> to the entraining case. With no entrainment, Garwood et al. <1985a, b> show that &OHgr;y effects can be substantial. The effects of &OHgr;y are small when the entrainment heat flux is significant. ¿ American Geophysical Union 1996