  We report the discovery of two spectroscopic binaries in the field of the old
open cluster M67 -- S1063 and S1113 -- whose positions in the color-magnitude
diagram place them approximately 1 mag below the subgiant branch. A ROSAT study
of M67 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. S1063 is also
projected within one core radius of the cluster center. S1063 is a single-lined
binary with a period of 18.396 days and an orbital eccentricity of 0.206. S1113
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 Mo main-sequence star, which implies a 1.3 Mo primary star. We
have been unable to explain securely the low apparent luminosities of the
primary stars; neither binary contain stars presently limited in radius by
their Roche lobes. 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.
