Few spacecraft observations of Pc3-4 (7--100 mHz) pulsations at L<3 have been reported, although ground observations of the pulsations in the same L range are routine. In particular, there are no systematic spacecraft observations of compressional pulsations expected at the time of low-latitude ground Pc3-4 pulsations that exhibit a constant frequency over a range of L. These pulsations have been attributed to fast mode waves trapped in the plasmasphere (referred to as plasmaspheric cavity mode waves) or to evanescent waves that exist inward of the turning point for fast mode waves propagating from the outer magnetosphere. We studied the properties of compressional Pc3-4 pulsations at L<3 using magnetic field data simultaneously acquired by the Active Magnetospheric Particle Tracer Explorers Charge Composition Explorer (AMPTE CCE) and at the Kakioka ground station (L=1.25) over a 2-year period from 1985 to 1986. From time intervals when the satellite was on the dayside and between L=2 and L=3, we identified 63 cases of magnetospheric compressional (bz) Pc3-4 pulsations with or without an accompanying perturbation in the radial (bx) component, depending on the latitude of the satellite. The pulsations were observed primarily when AMPTE CCE was at prenoon hours (magnetic local time (MLT)=0800--1200), and they were often accompanied by nearly identical magnetic pulsations at Kakioka. In an attempt to construct the spatial mode structure of the compressional pulsations, we have examined the relationship between the bx and bz components and also between the bz (or bx) component and the horizontal H (north-south) component at Kakioka. We find that the phase and amplitude relationship between bx and bz is consistent with waves standing in the meridian plane. The ground-satellite cross phase is clustered near the values expected for radially standing or evanescent waves but also exhibits considerable deviations from the expected values. Although we have demonstrated that compressional Pc3-4 pulsations exist in the low-L magnetosphere and that they give rise to pulsations on the ground, we conclude that further study is required to distinguish between the cavity and evanescent modes. ¿ 1999 American Geophysical Union