The orientation of the S-1 <-- S-0 <pi>,pi* transition dipole moments of oxonine (Ox(+)), pyronine (Py+), and POPOP (5,5'-diphenyl-2,2'-p-phenylenebis(oxazole)) in the channels of zeolite L crystals was investigated by means of fluorescence microscopy and single-crystal imaging. Qualitative observations led to the result that the transition moment of POPOP is aligned along the c-axis of the hexagonal crystals whereas the fluorescence of Ox(+) and Py+ is not. More detailed investigations on Ox(+) showed a cone-shaped distribution of the transition moments with a half-cone angle of 72 degrees. The orientation of the transition dipole moment for all of these molecules is parallel to the molecules' long axis. We found by means of space-filling arguments that POPOP, the van der Waals length of which is about 21 Angstrom, can only be aligned along the channel axis. This is in full agreement with the observed fluorescence anisotropy. For Ox(+) and Py+, geometrical arguments based on the zeolite L structure give room for only two possible arrangements of the molecules' long axis: a half cone angle of up to 40 degrees for Ox(+) and up to 30 degrees for Py+, and an angle of about 90 degrees for both of them with respect to the c-axis of zeolite L. The surprising discrepancy between geometrical considerations and the results of the fluorescence measurements can be explained by assuming that Ox(+) and Py+ are exposed to a considerable anisotropic electrical field in the zeolite channels.