We have searched the temperature maps from the COBE Differential Micro
wave Radiometers (DMR) first two years of data for evidence of unresol
ved sources. The high-latitude sky (Absolute value of b > 30-degrees)
contains no sources brighter than 192 muK thermodynamic temperature (3
22 Jy at 53 GHz). The cumulative count of sources brighter than thresh
old T, N(>T), is consistent with a superposition of instrument noise p
lus scale-invariant spectrum of cosmic temperature fluctuations normal
ized to Q(rms-PS) = 17 muK. We examine the temperature maps toward nea
rby clusters and find no evidence for any Sunyaev-Zel'dovich effect, D
ELTAy < 7.3 x 10(-6) (95% CL) averaged over the DMR beam. We examine t
he temperature maps near the brightest expected radio sources and dete
ct 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 densi
ty of any unresolved Planck-spectrum sources brighter than flux densit
y S, n(>S) < 2 x 10(4) (S/1 jy)-2 sr-1.