Abstract We have studied the magnetization dynamics induced by femtosecond optical pulses in ferromagnetic cobalt structures having different magneto-crystalline anisotropies. The detailed analysis of the initial magnetization trajectory reveals that, depending on this anisotropy, different paths are undertaken by the magnetization vector and that the initial phase of the precession motion is drastically modified. In addition, in cobalt films with an in-plane anisotropy axis, we observe an increase of the precession period when increasing the laser intensity. We attribute this behavior to a time dependent magneto-crystalline anisotropy due to the increase of the lattice temperature after the initial hot electron distribution induced by the femtosecond pulse relaxes to the lattice. These observations of the initial magnetization dynamics and of its following motion of precession are well explained by a dynamical model taking into account the non conservation of the magnetization modulus as well as the time dependent anisotropy due to the time dependent temperature. We also use this model to discuss limiting cases for the damping of the precession and of the recovery of the magnetization modulus in cobalt films and nanoparticles.