Summary: The most important characteristics of a nonlocal and nonlinear oscillator subject to dissipative forces are studied by means of an asymptotic perturbation method, based on temporal rescaling and harmonic balance. We determine the conditions under which bifurcations and limit cycles appear. If the parameters satisfy particular conditions, a quasi-periodic motion is predicted, because a second small frequency adds to the natural frequency of the oscillator. The analytical results are validated by numerically solving the original system.