We consider two oscillators with delayed direct and velocity coupling. The oscillators
have frequencies close or equal to 1:1 resonance. Due to the coupling the oscillations
of the subsystems are in or out of phase. For these synchronized and anti-phase solutions,
we use averaging for analytical stability results for small parameters. We also determine
bifurcation curves of the delay system numerically. We identify regions in the parameter
space (two coupling constants and the delay) where both solutions are stable or only
one. For small parameters the averaging and numerical results are in good agreement.
For larger values of the delay, we find multiple synchronized and anti-phase solutions.
For small detuning we show that a minimal coupling value is needed to have almost
synchronous or anti-phase behaviour.