Transient emission at energies near 1 MeV has been reported by previous experiments on time scales of weeks to months from the Galactic center, the Crab Nebula, and Cyg X-1, and on shorter time-scales from NGC 4151 and Cen A. The spectra of these events fall into two broad classes: a broad line-like feature centered near 1 MeV, and continuum emission (or a very broad feature) extending from ˜600 keV up to several MeV. These features have been interpreted theoretically in terms of emission from hot pair-dominated plasmas, which may be the necessary positron source implied by reports of narrow e- e+ annihilation lines from Cyg X- 1 and the Galactic center. In this paper, data accumulated by the Solar Maximum Mission Gamma Ray Spectrometer (GRS) between 1980 and 1989 have been searched for evidence of these two types of features. We find no compelling evidence for transient 1 MeV broad-line emission on time scales of order 12 d or longer when any of the sources are in the GRS field of view; upper limits on the transient line flux during any 12 d period are typically ˜4.5 × 10-3gamma (cm2 s)-1. The same is true of variability of the continuum between 0.6-7 MeV, for which the upper limits are characteristically ˜2 times the nominal flux from the Crab for any 12 d period. Our analysis was not sensitive enough either to confirm or to reject several reports from other experiments of transient emission in the 0.6-7 MeV continuum during 1980-1989. We withdraw the statement in Share et al. (1993) that our upper limit for one such event, a transient from the Crab Nebula in 1980 Spring, is inconsistent with the measurement of Ling & Dermer (1991). We did not detect any transient emission in the 1 MeV feature preceding or coinciding with reported emission of the 0.511 MeV annihilation line from the Galactic center in 1988-1989. We discuss briefly the implications of this result for models of the annihilation of positrons produced in the Galactic center source 1E 1740.7-2942