  We have searched the temperature maps from the COBE Differential Microwave
Radiometers (DMR) first two years of data for evidence of unresolved sources.
The high-latitude sky (|b| > 30\deg) contains no sources brighter than 192 uK
thermodynamic temperature (322 Jy at 53 GHz). The cumulative count of sources
brighter than threshold T, N(> T), is consistent with a superposition of
instrument noise plus a scale-invariant spectrum of cosmic temperature
fluctuations normalized to Qrms-PS = 17 uK. We examine the temperature maps
toward nearby clusters and find no evidence for any Sunyaev-Zel'dovich effect,
\Delta y < 7.3 x 10^{-6} (95% CL) averaged over the DMR beam. We examine the
temperature maps near the brightest expected radio sources and detect no
evidence of significant emission. The lack of bright unresolved sources in the
DMR maps, taken with anisotropy measurements on smaller angular scales, places
a weak constraint on the integral number density of any unresolved
Planck-spectrum sources brighter than flux density S, n(> S) < 2 x 10^4 (S/1
Jy)^{-2} sr^{-1}.
