Recent observations of angular distributions of TT mesons in p-p i, annihilation indicate a deviation from the predictions of the usual Fermi statistical model. In order to shed light on these phenomena, a modification of the statistical model is studied. We retain the assumption that the transition rate into a given final state is proportional to the probability of finding N free TT mesons in the reaction volume, but express this probability in terms of wave functions symmetrized with respect to particles of like charge. The justification of this assumption is discus sed. The model reproduces the experimental results qualitatively, provided the radius of the interaction volume is between one -half and three -fourths of the pion Compton wave length; the dependence of angular correlation effects on the value of the radius is rather sensitive. Quantitatively, there seems to remain some discrepancy, but we cannot say whether this is due to experi-. mental uncertainties or to some other dynamic effects. In the absence of information on TT-TT interactions and of a fully satisfactory explanation of the mean pion multiplicity for annihilation, we wish to emphasize the preliminary nature of our results. We consider them, however, as an indication that the symmetrization effects discussed here may well play a major role in the analysis of angular distributions although it is too early to say whether or -3-UCRL-9169 not these effects can account, quantitatively for the phenomena. It is pointed out that in this respect the ene'rgy dependence of the angular corre-