Using the BATSE instrument on the Compton Gamma Ray Observatory, the X
-ray bursters 4U 1820-30 and 4U 1915-05 have been monitored in the har
d X-ray band. In four years of data neither source was detected. We de
rive 2 sigma upper limits on 20-100 keV flux from 4U 1915-05 of 2.6 10
(-2) photons cm(-2) s(-1) (90 mCrab) for 1 day integrations and 9.0 10
(-3) photons cm(-2) s(-1) (30 mCrab) for 10 day integrations. For 4U 1
820-30 the upper limits are 2.4 10(-2) photons cm(-2) s(-1) (80 mCrab)
for 1 day integrations and 1.0 10(-2) photons cm(-2) s(-1) (30 mCrab)
for 10 day integrations. These limits are not strong enough to constr
ain spectral models for the sources. The implications of these observa
tions are discussed in light of BATSE results on other bursters.