Abstract
We interpret the three periods detected in OGLE LMC Cepheids SC3-360128 and SC5-338399 as corresponding to the first three overtones of radial pulsations. This interpretation imposes stringent constraints on parameters of the stars and on their evolutionary status, which could only be the first crossing of the instability strip. Evolutionary models reproducing measured periods exist only in a restricted range of metallicities (Z=0.004-0.007). The models impose an upper limit on the extent of overshooting from the convective core. Absolute magnitude of each star is confined to a narrow interval. This allows to derive a new estimate of the distance to the LMC. We obtain m-M ranging from 18.34mag to 18.53mag, with a systematic difference between the two stars of about 0.13mag. The rates of period change predicted by the models are formally in conflict with the derived observational limits, though the uncertainities of measured dP/dt may be underestimated. If the discrepancy is confirmed, it would constitute a significant challenge to the stellar evolution theory.
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