  We present the results of a search for variable stars in a 26x39 arcmin^2
field around globular cluster M79 (NGC1904). The search was made by means of an
extended version of image subtraction, which allows to analyze in a uniform
manner CCD frames obtained with different telescopes and cameras of different
sizes and resolutions. The search resulted in finding 20 new variable stars,
among which 13 are cluster members. The members include one new RR Lyr star of
subtype c, three SX Phe stars, and nine variable red giants. We also show that
V7 is a W Vir star with a period of 13.985 d. Revised mean periods of RRab and
RRc stars, <P_ab>=0.71 d and <P_c>=0.34 d, respectively, and relative
percentage of RRc stars, N_c/(N_ab+N_c)=45 % confirm that M79 belongs to the
Oosterhoff II group of globular clusters. The mean V magnitude of the
horizontal branch of M79 based on ten RR Lyr stars has been estimated to be
$V_HB=<V_RR>=16.11\pm0.03$ mag. In one RRc star, V9, light changes with three
close frequencies were detected, indicating excitation of nonradial modes. An
SX Phe star, V18, is a double-mode pulsator with two radial modes excited,
fundamental and first overtone. Moreover, we have discovered two SX Phe or
delta Sct stars and one W UMa type system, all likely field objects. We also
studied the period -- luminosity relation for SX Phe stars. Using 62
fundamental and fundamentalized periods of radial double-mode and
high-amplitude SX Phe stars known in Galactic globular clusters, we have
derived the slope and zero point of this relation to be, $-3.35\pm0.24$ and
$2.68\pm0.03$ mag (at log(P/d)=-1.24), respectively.
