The generic isolated bifurcation for one-parameter families of smooth planar vector fields which give rise to periodic orbits are : the Andronov-Hopf bifurcation, the bifurcation from a semi-stable periodic orbit , the saddle-node loop bifurcation and the saddle loop bifurcation. In this paper we obtain the dominant term of the asymptotic behaviour of the period of the limit cycles appearing in each of these bifurcations in termes of when we are near the bifurcation.