AbstractA short-lived (weeks-months) burst of radio emission, assumed to be synchrotron radiation, is sometimes associated with objects detected as soft X-ray transients. The “synchrotron bubble model” which has been applied to these radio transients assumes that the source is initially optically thick, and the model therefore takes no account of the details of the electron acceleration required. The initial increase in the radio flux is attributed to decreasing absorption in the expanding source. Observations of the soft X-ray transient GRS 1124 – 68 (X-ray Nova Muscae 1991) showed, for the first time, the rising phase of such a radio transient. Another radio source, the Galactic Center Transient, was discovered serendipitously in the radio and observed throughout its rise and decay. In both cases the radio flux was a decreasing function of frequency throughout the periods of increasing and decreasing flux, which is not consistent with the optically thick assumption of the synchrotron bubble model. When this assumption is discarded the mechanism responsible for producing the ultrarelativistic electrons, or at the very least the rate at which those electrons become available, must be considered. A generalization of the simple model to include a source which supplies relativistic electrons with a constant energy spectrum is discussed. While such a model can go some way toward matching the observations, it is suggested that the time is ripe for an explicit model of the electron acceleration mechanism. Some of the features such a model may have are presented.Subject headings: acceleration of particles — radio continuum: general — radiation mechanisms: nonthermal — X-rays: bursts