Excitation and emission polarization dependence of fluorescence intensity of single LH2 complexes from Rhodopseudomonas acidophila 10050 and Rhodobacter sphaeroides is reported. The results are presented as two-dimensional polarization plots and interpreted in terms of tilted light harvesting complexes indicating that sample preparation leads to partially oriented LH2 cylinders. An alternative explanation of the observation can be structural deformation. Fluorescence intensity of the complexes has four qualitatively distinct excitation emission polarization dependencies. The differences in excitation polarization dependence are interpreted as due to the tilt of the complexes, whereas the emission polarization behavior is mainly determined by spectral inhomogeneity of the emitting B850 ring. Some complexes show abrupt reversible variations of the total emission intensity together with changes of the polarization properties which cannot be described by the simplest model of tilted LH2s with spectral disorder.