An arrangement for fluorescence microscopic examination of specimens includes: a fluorescence microscope; an illumination device that includes: a housing including an interface configured to optically couple the housing and the fluorescence microscope; a plurality of light-emitting diodes disposed in the housing; a respective collector disposed downstream of each of the light emitting diodes and configured to generate a directed light flux; and at least one dichroic splitter disposed in the housing, the at least one splitter and the light-emitting diodes being spatially disposed with respect to one another so that the directed light fluxes are combinable via the at least one splitter into a common illumination beam path directed onto the interface; and a logical control device common to the fluorescence microscope and the illumination device.