Overcontact binary is a kind of close binary where both components filling the critical Roche lobe and sharing a CCE（Common Convective Envelope）. The degree of overcontact f is a physical quantity that describes how much the mass of the components fill the inner critical surface and the outer critical surface. Shallow-contact binary is a kind of system whose f is less than 20%. Shallow-contact binary is a bridge between the overcontact binary and the semi-detached binary. In this paper, some binaries were observed, analyzed. The shallow-contact binaries are studied statistically. The results are obtained as follow: 1. It is discovered that RV Psc and BI CVn are shallow-contact binaries with the period decreasing. Their degrees of overcontact and period decrease rates are 5.8% and 18.0%, -5.89x10-8days/year and -1.51 x10-7days/year, respectively. This indicated that the mass transfer from the primary to the secondary component. This suggests that they were formed from short-period detached binaries via a Case A mass transfer. As the shrinking of the Roche lobe continues (because of the decrease of the orbital period), the formation of a CCE will cause them evolve into normal overcontact binary stars. 2. We find AE Phe is a shallow-contact binary with the period increasing continuously at a rate of +5.50 x10-8days/year. The degree of overcontact of AE Phe is 14.6%. The long-term period increase may suggest that AE Phe is on the TRO-controlled stage of the evolutionary scheme. The long-term period increase, the shallow-contact configuration, and the astrophysical parameters of the binary system, all suggest that it is a shallow-contact binary on the thermal relaxation oscillation evolving into a detached binary. 3. It is found that DM Del is a semi-detached binary with a lobe-filling primary with period decrease rates -2.68 x10-7days/year. DM Del evolves into semi-detached configuration via AML and a Case A mass transfer occurs after the original more massive component filling its critical Roche lobe. The geometrical structure and the long-term period decrease suggest that DM Del may be a progenitor of overcontact binary or just in a broken-contact stage predicted by thermal relaxation oscillations. And DM Del will evolve into a shallow-contact binary with the period decreasing. 4. We find BS Cas and RT LMi are middle-contact binaries with the period decreasing continuously. Their degrees of overcontact and period decrease rates are 27.5% and 28.2%, -1.51 x10-7days/year and -1.64 x10-8days/year, respectively. The long-term orbital period decrease suggests that BS Cas and RT LMi are undergoing mass transfer from the primary component to the secondary one. With the mass transfers and accompanying angular momentum loss, the binaries will evolve into deeper contact configuration. 5. We find that more than 50% contact binaries belong to shallow-contact binaries; the later the spectral type, the more shallow-contact binaries; more than two thirds of shallow-contact binaries belong to W-type contact binaries.
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