It is found that the initial rise of far-field P wave velocity pulses generated by microearthquakes is not well represented by a ramp function but exhibits a gradual increase according to the function t″ (2<n<4), where t is the time measured from the onset of the P wave. This slow rise, termed the slow initial phase, is detected in all 69 earthquakes analyzed here. Their seismic moments range between 108 and 1013 Nm. No ramplike onsets are observed, suggesting that the slow rise is not an anomalous feature but is always generated by earthquakes of this size. The slow initial phase is not due to the transient response of the recording system. Analyses and simulations suggest that the slow initial phase is also not likely to result from an inhomogenuous velocity structure but that it may be partly due to anelastic attenuation. The slow initial phase likely results from the source process of the microearthquakes, especially those instances of the phase with a longer duration. The slow initial phase cannot be explained by theoretical source models which assume constant dynamic friction and rupture velocity in an expanding fault. This is because these models predict a ramplike behavior in the initial rise of the far-field P wave velocity pulse. Only the observed ramplike waveform following the slow initial phase can be explained by these models. The slow initial phase can be explained by models which predict slow slip velocities and/or rupture velocities immediately after rupture initiation, such as the slip-weakening crack model. The duration of the slow initial phase is proportional to the rise time of the P wave velocity pulse. This dependence implies that longer, slow initial phases are generated by larger earthquakes, the duration of the slow initial phase being a measure of the earthquake size. ¿ American Geophysical Union 1995