We report the discovery of two spectroscopic binaries in the field of the old open cluster M 67 – S 1063 and S 1113 – whose positions in the color-magnitude diagram place them \approx 1 mag below the subgiant branch . A ROSAT study of M 67 independently discovered these stars to be X-ray sources . Both have proper-motion membership probabilities greater than 97 % ; precise center-of-mass velocities are consistent with the cluster mean radial velocity . S 1063 is also projected within one core radius of the cluster center . S 1063 is a single-lined binary with a period of 18.396 days and an orbital eccentricity of 0.206 . S 1113 is a double-lined system with a circular orbit having a period of 2.823094 days . The primary stars of both binaries are subgiants . The secondary of S1113 is likely a 0.9 M _ { \odot } main-sequence star , which implies a 1.3 M _ { \odot } primary star . We have been unable to explain securely the low apparent luminosities of the primary stars . The colors of S1063 suggest 0.15 mag higher reddening than found for either M67 or through the entire Galaxy in the direction of M67 . S1063 could be explained as an extincted M67 subgiant , although the origin of such enhanced extinction is unknown . The photometric properties of S1113 are well modeled by a cluster binary with a 0.9 M _ { \odot } main-sequence secondary star . However , the low composite luminosity requires a small ( 2.0 R _ { \odot } ) primary star that would be supersynchronously rotating , in contrast to the short synchronization timescales , the circular orbit , and the periodic photometric variability with the orbital period . Geometric arguments based on a tidally relaxed system suggest a larger ( 4.0 R _ { \odot } ) primary star in a background binary , but such a large star violates the observed flux ratio . Thus we have not been able to find a compelling solution for the S1113 system . We speculate that S1063 and S1113 may be the products of close stellar encounters involving binaries in the cluster environment , and may define alternative stellar evolutionary tracks associated with mass-transfer episodes , mergers , and/or dynamical stellar exchanges .