We present upper limits from CGRO Oriented Scintillation Spectrometer
Experiment (OSSE) observations of pulsars and a summary of pulsar obse
rvations made with the Compton Gamma Ray Observatory (CGRO). We also r
eport an upper limit to phase-averaged emission for the globular clust
er 47 Tuc which is thought to contain many millisecond pulsars. The 2
sigma upper limit is 3 x 10(-5) photons cm(-2) s(-1) keV(-1) in the 50
-150 keV energy range. The best predictor of a pulsar having a detecta
ble gamma-ray emission appears to be the X-ray luminosities observed b
y the Rontgen Satellite (ROSAT) (similar to 0.1-2.4 keV) or the Einste
in satellite (similar to 0.1-4.0 keV). We compare the gamma-ray data t
o models related to the inferred magnetic field, the spin-down rate, a
nd/or the frequency. Apparent correlations indicated by the pulsars de
tected by OSSE and the CGRO Energetic Gamma-Ray Experiment Telescope (
EGRET) have counterexamples in all cases.