Consider the two-dimensional system \[ \frac{dx}{dt}=f(x,\epsilon), \] where \(f(0,\epsilon)=0\). In the supercritical Andronov-Hopf theory, one imposes conditions to ensure that \(x=0\) is an exponentially asymptotically stable equilibrium point for \(\epsilon < 0\), and for small positive \(\epsilon\), there is an exponentially asymptotically stable periodic solution with non-zero minimal period, at a distance \(O (\sqrt{\epsilon})\) from the origin. The authors consider some conditions under which the Andronov-Hopf bifurcation persists for the nonautonomous perturbation \[ \frac{dx}{dt}= f(x,\epsilon)+\mu g(t,x,\epsilon, \mu) \]