  We report on the discovery of the second case of a galactic Cepheid,
ASAS112843-5925.7=HD 304373, pulsating in the the first (1O) and second (2O)
radial overtones. The ratio between the periods (0.8058), the short value of
the 1O period (0.922405 d) and the shape of the 1O light curve makes HD 304373
very similar to the 1O/2O Cepheids in the Magellanic Clouds. The implications
of a so close similarity between a galactic 1O/2O pulsator and LMC ones are
discussed in terms of importance of the metallicity effects.
