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New eight times of minimum light of the near-contact binary EG Cep were presented. All times of minimum light for EG Cep, including ours, were collected and analyzed to study it's orbital period variation. It was found that the orbital period have varied in a cyclical way superposed on an upward parabola. A secular period increase of 3.22 times 10^{-8} d/y was calculated. Under the assumption of a conservative mass transfer, it implied that the stellar gaseous material of about 3.18 times 10^{-8} rm M_odot /year is transferring from the less massive secondary component to the primary. The cyclical period variation was interpreted as light-time effect due to an unseen third body in the system. The resultant period, semi-amplitude and eccentricity of the light time orbit were calculated to be 38.^{rm y}4, 0.^{rm d}0034 and 0.29, respectively. The mass range of the tertiary proposed in the system is deduced to be quite small as 0.10M_{odot} leq M_3 leq 0.21M_{odot} for i_3 g

A PERIOD STUDY OF THE NEAR CONTACT BINARY EG CEP