  We observed two fields near M32 with the ACS/HRC on board the Hubble Space
Telescope, located at distances of about 1.8' and 5.4' (hereafter F1 and F2,
respectively) from the center of M32. To obtain a very detailed and deep
color-magnitude diagram (CMD) and to look for short period variability, we
obtained time-series imaging of each field in 32-orbit-long exposures using the
F435W (B) and F555W (V) filters, spanning a temporal range of 2 days per
filter. We focus on our detection of variability on RR Lyrae variable stars,
which represents the only way to obtain information about the presence of a
very old population (larger than 10 Gyr) in M32 from optical data. Here we
present results obtained from the detection of 31 RR Lyrae in these fields: 17
in F1 and 14 in F2.
