We present a detailed analysis of high resolution measurements of the specific heat anomalies at the Tc of three YBa2Cu3O7-δ-samples. The anomalies can be described by the sum of a mean field (MF) step and a contribution from gaussian fluctuations of the order parameter. These fluctuations are threedimensional (3D) near Tc and show a crossover to 2D-behaviour some K away from Tc. By means of a Lawrence-Doniach type description of the fluctuations we estimate the anisotropic coherence lengths ξ and ξ⊥. The values are consistent with data of the fluctuation contribution to the susceptibility above Tc. We give data for ΔCMF and discuss the relevance of critical fluctuations. The influence of the oxygen content δ on the broadening and splitting of the transition is shown.