  XZ Ceti is the only known anomalous Cepheid in the Galactic field. Being the
nearest and brightest such variable star, a detailed study of XZ Ceti may shed
light on the behaviour of anomalous Cepheids whose representatives have been
mostly detected in external galaxies. CCD photometric and radial velocity
observations have been obtained. The actual period and amplitude of pulsation
were determined by Fourier analysis. The long time scale behaviour of the
pulsation period was studied by the method of the O-C diagram using the
archival Harvard photographic plates and published photometric data. XZ Ceti
differs from the ordinary classical Cepheids in several respects. Its most
peculiar feature is cycle-to-cycle variability of the light curve. The radial
velocity phase curve is not stable either. The pulsation period is subjected to
strong changes on various time scales including a very short one. The ratio of
amplitudes determined from the photometric and radial velocity observations
indicates that this Cepheid performs an overtone pulsation, in accord with the
other known anomalous Cepheid in our Galaxy, BL Boo (V19 in the globular
cluster NGC 5466). Continued observations are necessary to study the deviations
from regularity, to determine their time scale, as well as to confirm binarity
of XZ Ceti and to study its role in the observed peculiar behaviour.
