A burner device having a burner chamber (26) filled at least partially by a porous body (28), an evaporation zone (12) upstream of the burner chamber (26) for evaporating liquid fuel supplied via a fuel inlet line (16), an igniter (30) for igniting a combustion mixture of evaporated liquid fuel and combustion air supplied via a combustion air inlet line (18) to the evaporation zone (12) as well as an exhaust discharge (38) downstream of the combustion chamber (26). A mixing zone (20) is disposed between the evaporation zone (14) and the combustion chamber (26) in which fuel gas is introduced via a fuel gas inlet line (22, 24) and is mixed with the combustion air and/or the combustion mixture. The burner device can be used as an afterburner in a fuel cell stack.