The fluorescence anisotropy of two neutral and nonpolar molecules, 2,5,8,11-tetra-tert-butylperylene (TP) and 2,5,10,13-tetra-tert-butylterrylene (TT), is studied in a series of n-alcohols and alkanes. Both probes show an absorption band in the UV region and one in the visible region. The polarized fluorescence decay traces are globally analyzed over different excitation wavelengths. TP and TT can be modeled as oblate ellipsoids with essentially identical rotational correlation times. The anisotropy decay can well be approximated by a monoexponential model for both solvent series. The rotational correlation times (phi) vary linearly with viscosity (eta) for both solvent series. Higher values for phi/eta are reached in alkanes than in alcohols, the effect being more pronounced for TP than for TT. The predictions of the quasihydrodynamic models of Gierer-Wirtz and of Dote-Kivelson-Schwartz (DKS) are compared to the experimental data. Only the DKS model can predict qualitatively the experimental observations. The difference in rotational correlation times can be explained in terms of the higher free volume in alcohols than in alkanes. Anisotropy decay measurements of TT in hexadecane and decanol in the temperature range 25-60 degrees C give additional support to the applicability of the DKS theory for nonpolar solutes and suggest that an Arhenius formalism to calculate the activation energy for rotation from the SDE equation is not appropriate when solute and solvent molecules are of similar magnitude.