Abstract The orbital period of the short-period eclipsing binary DM Del was analyzed by using two newly determined eclipse times together with the others compiled from the literature. It has been discovered that the period shows a long-time continuous decrease at a rate of $dP/dt = -$2.27 $\times$ 10$^{-7}$ d yr$^{-1}$, while it undergoes a cyclic variation with a period of 31.73 years. Meanwhile, photometric light curves of a close binary in the $B$ and $V$ bands, published by Güdür et al., were analyzed with the 2003 version of the W–D code. It was found that the system is a semi-detached binary with a lobe-filling primary and a mass ratio of $q =$ 0.55. The long-time period decrease can be explained by mass transfer from the primary to the secondary. This is consistent with the semi-detached configuration. The geometrical structure of the binary and the long-term period decrease suggest that DM Del may be a progenitor of an overcontact binary or just in a broken-contact stage predicted by thermal relaxation oscillations. A cyclic period change reveals the presence of a tertiary unseen companion that may play an important role in the formation of the close binary by removing angular momentum from the central system.
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