In this paper we present the behaviour of the magnetocrystalline anisotropy constants of [Co Pt ]6 multilayers as a function of temperature, ex-32A ternal magnetic field, and no xA n-magnetic layer thickness, observed by means of a torque magnetometer in an in-plane configuration. We have determined the magnetocrystalline anisotropy constants from the magnetic torque curves for different temperatures and in different magnetic fields, taking into account the angle difference between the directions of the external field and the magnetization. Among the results of this paper there are the determination of the critical thickness of Pt and the need to introduce the third order anisotropy constant in the analysis.