We study properties of an accretion ring in a steady mass flow from a companion star to a compact object in an X-ray binary. The accretion ring is a place where matter inflowing from a companion star sojourns for a while to bifurcate to accretion and excretion flows due to angular momentum transfer in it. The matter in the accretion ring rotates along the Keplerian circular orbit determined by the intrinsic specific angular momentum of the inflowing matter and forms a thick ring-envelope. Two internal flows are expected to appear in the thick envelope. One is a mass spreading flow bifurcating to a thick accretion flow and a thick excretion flow, as a result of the angular momentum transfer within the ring-envelope. The other is a cooling flow toward the envelope center governed by radiative cooling under an effect of X-ray irradiation. This cooling flow eventually forms a core in the torus, from which a thin accretion disk and a thin excretion disk spread out as a result of the angular momentum transfer there again. Evaluating and comparing the time scales for the two internal flows, the accretion ring is shown to generally originate a two-layer accretion flow in which a thin accretion disk is sandwiched by a thick accretion flow, unless the accretion rate is very low. Properties of the thin excretion disk and the thick excretion flow are also investigated. The thin excretion disk is expected to terminate at a distance 4 times as large as the accretion ring radius and to form another ring there, unless tidal effects from the companion star exist. The thick excretion flow is, on the other hand, likely to turn to a super-sonic wind-flow reaching the infinity.
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