The presence of scintillation-producing irregularities in the nighttime equatorial ionosphere, in the path of Global Positioning System (GPS) signals received at an equatorial station, causes dual-frequency measurements of the differential carrier phase of GPS L1 and L2 signals to have a contribution from phase scintillations on the two signals. Dual-frequency data for fluctuations in the total electron content (TEC) along the path of GPS signals to the equatorial station Ancon (1.5¿ dip), sampled at a rate of 1 Hz, are used to separate this contribution from the slower TEC variations. Rapid fluctuations in the differential carrier phase, usually on timescales <100 s, which result from diffraction, are seen to follow the pattern of intensity scintillations on the L1 signal. Intensity scintillations are also related to the variations in TEC which arise from density fluctuations associated with ionospheric irregularities. An approximate version of the transport-of-intensity equation, based on a phase screen description of the irregularities, suggests that a quantitative measure of intensity scintillations may be provided by the derivative of rate of change of TEC index (DROTI), obtained from the second derivative of TEC. This equation also yields the dependence of the scaling factor between DROTI and S4 on the Fresnel frequency. Comparison of DROTI computed from relative TEC data to corresponding S4 indices indicates that there may be lesser uncertainty in a quantitative relation between the two than between the index ROTI, introduced in recent years, and S4. Power spectral analysis of TEC fluctuations and simultaneous intensity scintillations on L1 signal, recorded at Ancon, does not indicate any simple dependence of the scaling factor between DROTI and S4 on the spectral characteristics. ¿ 2000 American Geophysical Union