Microporous materials containing linear channels running through hexagonal microcrystals allow the formation of very concentrated monomeric and highly anisotropic oriented dye systems that support extremely fast energy migration. Energy migration can be described as a homogeneous Markoffian random walk, in which each energy transfer step is incoherent and occurs from a thermalized initial state. The dyes investigated have an electronic transition dipole moment mu s(1)-s(0) which coincides with their long axes. The individual energy transfer steps calculated based on dipole-dipole interactions occur with rate constants of up to 30 ps(-1). This fast energy migration cannot be described by a diffusive process immediately after irradiation but becomes diffusive after several tenths of a picosecond. After this time a constant diffusion coefficient D can be defined with values of up to about 0.3 cm(2) S-1 for an optimized system based on, for example, cylindrical zeolite L microcrystals and oxonine. A main part of this study refers to excitation trapping on the surface of cylindrical microcrystals. We distinguish between front trapping (traps positioned on the front of the cylinders), front-back frapping (traps on the front and on the back), coat trapping (traps on the coat), axial trapping (traps located in the central channel), and point trapping (a single trap at the center of the front). In cylindrical microcrystals with a size of 50 nm containing about 33,000 chromophores and complete coverage of the outer surface by traps, a total trapping efficiency of 99.8% can be obtained. The front-back trapping efficiency is 60.4% and the coat trapping efficiency is 39.4%. The front trapping efficiencies reach 99.0% if only the front is covered by traps. In a microcrystal of 37 nm length, still containing 12,600 chromophores, point trapping efficiencies of up to 93.0% have been calculated.