  For seven years, the EROS-2 project obtained a mass of photometric data on
variable stars. We present a peculiar Cepheid-like star, in the direction of
the Small Magellanic Cloud, which demonstrates unusual photometric behaviour
over a short time interval. We report on data of the photometry acquired by the
MARLY telescope and spectroscopy from the EFOSC instrument for this star,
called EROS2 J005135-714459(sm0060n13842), which resembles the unusual Cepheid
HR 7308. The light curve of our target is analysed using the Analysis of
Variance method to determine a pulsational period of 5.5675 days. A fit of
time-dependent Fourier coefficients is performed and a search for proper motion
is conducted. The light curve exhibits a previously unobserved and spectacular
change in both mean magnitude and amplitude, which has no clear theoretical
explanation. Our analysis of the spectrum implies a radial velocity of 104 km
s$^{-1}$ and a metallicity of -0.4$\pm$0.2 dex. In the direction of right
ascension, we measure a proper motion of 17.4$\pm$6.0 mas yr$^{-1}$ using EROS
astrometry, which is compatible with data from the NOMAD catalogue. The nature
of EROS2 J005135-714459(sm0060n13842) remains unclear. For this star, we may
have detected a non-zero proper motion for this star, which would imply that it
is a foreground object. Its radial velocity, pulsational characteristics, and
photometric data, however, suggest that it is instead a Cepheid-like object
located in the SMC. In such a case, it would present a challenge to
conventional Cepheid models.
