W Ursae Majoris (W UMa) contact binaries are eclipsing variables in which two components are in contact or over°owing their Roche limiting surfaces. Two components ofWUMa contact binaries share a common convective envelope，and their effective temperature are nearly identical. Therefore，WUMa binaries show EW-type light curves. Based on the physical parameters of 133 W UMa contact binaries, the energy transfer and its effects on the secondaries in W UMa contact binaries are investigated. In addition, using Eggleton's stellar evolution code, we study the minimum mass ratio (qmin) of W UMa contact binaries under the different primary masses. We also investigate the mass loss during the merging process of W UMa-type systems and calculate the rotation cities of the single stars formed by the merger of W UMa contact binaries due to tidal instability. some results are obtained as the follows: 1. Relations between the mass ratio (q) for W UMa contact binaries and the relative energy transfer rates（i.e. U1, the ratio of the transferred luminosity to the surface luminosity of the primary and U2, the ratio of the transferred luminosity to the nuclear luminosity of the secondary）are given . The theoretical curves (U1-q and U2-q) are derived based on the various assumptions, such as two components in each W UMa system are nearly identical in effective temperature, they just ¯ll their inner Roche lobes, and the primaries are zero-age main sequence （ZAMS）stars. Although these curves can reflect the distribution of U1-q and
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