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 \aas@@fstack { m } 34 to 18 \aas@@fstack { m } 53 , with a systematic difference between the two stars of about 0 \aas@@fstack { m } 13 .
The rates of period change predicted by the models are formally in conflict with the derived observational limits , though the uncertainities of measured \dot { P } may be underestimated .
If the discrepancy is confirmed , it would constitute a significant challenge to the stellar evolution theory .