A model of two predators competing for a single prey is considered. Taking into account several factors as growth and death rates, and intraspecific competition, a system of three delay-differential equations is derived. Moreover, periodic coefficients are included to involve the effect of changing environment. However, no interaction between the two predators is assumed. The main achievements of this paper are an existence result in which sufficient conditions are found to ensure that there is at least one positive periodic solution to the system, and a result stating that the periodic solution is unique and globally attracting under some additional assumptions. The principal tools used are degree theory and the construction of a Lyapunov function.