  Accurate CCD observations of three Cepheids in the SMC were made with the
purpose of confirming their nature of second overtone mode Cepheids. The stars
were suspected pulsating in the second overtone mode owing to the unusual light
curve and short period reported by Payne-Gaposchkin & Gaposchkin (1966). The
analysis of the new data shows that for two stars the previous periods are
wrong, and in the three cases the new light curves are normal. According to the
new observations, HV 1353 is a fundamental mode pulsator with small amplitude,
and HV 1777 and HV 1779 are first overtone mode pulsators.
  Also the star HV 1763, whose nature was unknown, was observed in the field of
HV 1777. The new data show that it is a first overtone mode Cepheid with
P=2.117d.
