Context : 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 .

Aims : 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 .

Methods : 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 .

Results : 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 .

Conclusions : 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 .