The theory of binary star evolution suggests that approximately 10% of all main-sequence binary systems should evolve into a close pair of light white dwarfs which merge within a Hubble time. This paper explores the consequences of such mergers on the assumption that a merger can be approximated by a mass-transfer event which occurs on a time scale shorter than that given by the Eddington accretion limit. It is shown that, if both white dwarfs are made of helium (He) and if the total mass of the merging white dwarf pair is larger than a critical value (<0.38 M⊙, and probably of order 0.3 M⊙), then, following the termination of the merging episode, helium is ignited at the base of the accreted layer and burning works its way to the center in a series of mild flashes. The net result is a helium star which evolves in the H-R diagram through a region occupied by the low-luminosity, high-temperature portion of the sdO star distribution. If it is assumed that enough hydrogen caught at the interface of the merging pair survives burning and diffuses to the top, then the models can also account for some portion of all sdB stars. The predicted space density of merged binaries in number versus mass exceeds the observationally based estimate of this density by a factor of 3 or more. The predicted space density of subdwarfs brighter than 10 L⊙ exceeds the observationally based estimate by a factor of about 2. If the more massive white dwarf is a hybrid (i.e., if there is a substantial helium layer above a carbon-oxygen core) or is composed primarily of carbon and oxygen (CO), then merger with a helium white dwarf results initially in a luminous, cool star. The more massive products evolve in the H-R diagram in the vicinity of observed R CrB stars and other, hotter hydrogen-deficient stars. The less massive products evolve through the high-luminosity, low-surface temperature portion of the region defined by observed sdO stars. A major lesson of the numerical exercises, derived by comparing models of the same CO core mass and total mass, but of different origin (merger of a hybrid or CO white dwarf with a He white dwarf as opposed to He + He white dwarf mergers), is that the location of a model (and therefore possibly also of a real star) in the H-R diagram can be an extremely sensitive function of the prior thermal history of the star (hot white dwarf core in the case of He + He mergers, cold white-dwarf core in the case of He + CO or He + hybrid mergers).
