  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.
