We report on the discovery of the second case of a galactic Cepheid , ASAS 112843 –5925.7 \equiv 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 .