A catalytically operating burner with a catalyzer structure (4), useful in particular for a gas turbine system, has a heat-resistant carrier material (10) that forms the walls of several adjoining channels (13). The channels (13) pervade the catalyzer structure (4) in longitudinal direction and permit that a gaseous reaction mixture flows through the catalyzer structure (4). The walls are coated at least in part with a catalyst. In order to improve the catalytic conversion within the catalyzer structure (4), communicating openings (14) are constructed in the walls between an inlet end and an outlet end of the catalyzer structure (4). Adjoining channels (13) are able to communicate with each other through the communicating openings (14).