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A system of averaged equations for two oscillators, similar to reported in [1], but with delay in coupling is considered. It is shown that for certain values of delay ("resonant" delay), the system is associated with the Hamiltonian one and may be investigated by an approach, proposed in [2]. An analytical criterion of destruction the separatrix loops, originating from a saddle-focus stationary point is proposed basing on the Melnikov method. [1]Y. Tsarin: Various orders of resonances and chaos in a two-mode quasilinear system, XXV Dynamics Days Europe, Germany, (2005). [2]L. Lerman, Y. Umansky: About existence of separatrix loops in 4D systems closed to Hamiltonian integrable ones, Prikl.Math&Mech, 47, p.395 (1983)