A detailed analysis of orbital period changes of seven near-contact binary stars (NCBs) (BL And, V473 Cas, XZ CMi, BV Eri, RU Eri, UU Lyn and GR Tau) with period less than 1 d has been performed and their respective O-C diagrams are formed and discussed. It is found that all systems analysed show secular period decreasing. For V473 Cas, the analysis of the period change was performed based on data collected by Moschner, Frank & Bastian. For XZ CMi, its period shows some complex changes, a possible cyclic oscillation is discovered to superpose on the secular decrease that can be explained either by the presence of a third body or by magnetic activity cycles of the components. Since the third-body assumption is consistent with the photometric solution of Rafert, XZ CMi may be a truly triple system. For BV Eri, the period decrease is only supported by weak evidence. All the seven systems are short-period NCBs with AF-type primary components where both components are filling or nearly filling the critical Roche lobe. As the period decreases, the separation between both components will be reducing and thus these systems will evolve into A-type overcontact binaries. The period decrease may be caused by mass transfer or/and by angular momentum loss via magnetic braking. Combined with the published data on the other systems of the same type, a possible statistical connection between orbital period P and its rate of decrease dP/dt is obtained: dP/dt=-5.3 × 10-7×P+ 1.3 × 10-7 d yr-1. This correlation indicates that the smaller the orbital period P is, the smaller its rate of change dP/dt will be. The correlation found in this paper indicates that there may be a smooth transition from A- and F-type NCBs with period decreases to the A- and F-type overcontact binaries that have period increases, and in that sense one may postulate that the NCBs may be the progenitors of the A-type W UMa systems and will be oscillating around a marginal-contact state as predicted by thermal relaxation oscillation (TRO) theory.