Analysis of the dayside electron density (Ne) and neutral mass density (N) at 400km height measured by CHAMP during 12 intense geomagnetic storms in 2000-2004, and ion densities at 600km and 840km heights measured by ROCSAT and DMSP during a few of the intense storms, reveal some new aspects. Thermospheric storms (change of N) reach the equator within 1.5 to 3 hours from the main phase (MP) onset of intense storms having short and steady MPs. The responses of the equatorial ionosphere (at CHAMP) to both MPs and RPs (recovery phases) of the storms are generally opposite to those at higher latitudes. In addition to the known opposite responses during MPs, the analysis reveals that positive ionospheric storms develop at equatorial latitudes (within about ±15° magnetic latitudes) during daytime RPs, while conventional negative storms occur at higher latitudes. Ionospheric storms also extend to the topside ionosphere beyond 850km height and are generally positive (at DMSP), especially during MPs. The positive storms around the equatorial ionospheric peak during RPs are interpreted in terms of the potential sources such as (1) zero or westward electric fields due to disturbance dynamo and/or prompt penetration, (2) plasma convergence due to the mechanical effects of storm-time equatorward neutral winds and waves, (3) increase of atomic oxygen density and decrease of molecular nitrogen density due to the downwelling effect of the winds, and (4) photoionization. The positive storms in the topside ionosphere during MPs involve the rapid upward drift of plasma due to eastward PPEFs, reduction in the downward diffusion of plasma along the field lines, and plasma convergence due to equatorward winds and waves.