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We have obtained extensive high-quality spectroscopic observations of theOGLE-LMC-CEP-1718 eclipsing binary system in the Large Magellanic Cloud whichSoszynski et al. (2008) had identified as a candidate system for containing twoclassical Cepheids in orbit. Our spectroscopic data clearly demonstrate binarymotion of the Cepheids in a 413-day eccentric orbit, rendering this eclipsingbinary system the first ever known to consist of two classical Cepheidvariables. After disentangling the four different radial velocity variations inthe system we present the orbital solution and the individual pulsationalradial velocity curves of the Cepheids. We show that both Cepheids areextremely likely to be first overtone pulsators and determine their respectivedynamical masses, which turn out to be equal to within 1.5 %. Since thesecondary eclipse is not observed in the orbital light curve we cannot derivethe individual radii of the Cepheids, but the sum of their radii derived fromthe photometry is consistent with overtone pulsation for both variables.  The existence of two equal-mass Cepheids in a binary system having differentpulsation periods (1.96 and 2.48 days, respectively) may pose an interestingchallenge to stellar evolution and pulsation theories, and a more detailedstudy of this system using additional datasets should yield deeper insightabout the physics of stellar evolution of Cepheid variables. Future analysis ofthe system using additional near-infrared photometry might also lead to abetter understanding of the systematic uncertainties in current Baade-Wesselinktechniques of distance determinations to Cepheid variables.

The Araucaria Project. OGLE-LMC-CEP-1718: An exotic eclipsing binary system composed of two classical overtone Cepheids in a 413-day orbit