The BL Lacertae object Markarian 501 was identified as a source of gamma-ra
y emission at the Whipple Observatory in 1995 March. Here we present a flux
variability analysis on several timescales of the 233 hr data set accumula
ted over 213 nights (from March 1995 to July 1998) with the Whipple Observa
tory 10 m atmospheric Cerenkov imaging telescope. In 1995, with the excepti
on of a single night, the flux from Markarian 501 was constant on daily and
monthly timescales and had an average flux of only 10% that of the Crab Ne
bula, making it the weakest very high energy source detected to date. In 19
96, the average flux was approximately twice the 1995 flux and showed signi
ficant month-to-month variability. No significant day-scale variations were
detected. The average gamma-ray flux above similar to 350 GeV in the 1997
observing season rose to 1.4 times that of the Crab Nebula-14 times the 199
5 discovery level-allowing a search for variability on timescales shorter t
han 1 day. Significant hour-scale variability was present in the 1997 data,
with the shortest, observed on MJD 50,607, having a doubling time of simil
ar to 2 hr. In 1998 the average emission level decreased considerably from
that of 1997 (to similar to 20% of the Crab Nebula flux), but two significa
nt flaring events were observed. Thus the emission from Markarian 501 shows
large amplitude and rapid flux variability at very high energies, as does
Markarian 421. It also shows large mean flux level variations on year-to-ye
ar timescales, behavior that has not been seen from Markarian 421 so far.