A burner assembly with a combustion chamber, a plurality of mixing ducts leading into the combustion chamber, where combustion air and introduced fuel are mixed. The mixing ducts are formed by mixing tubes extending axially through an annular space between a tubular outer wall, a tubular inner wall arranged radially at a distance from the outer wall, a ring-shaped end plate arranged upstream and a ring-shaped end plate arranged downstream. The end plates have through-openings, which accommodate and/or extend the mixing tubes, and the end plates have, both radially inside and outside, a circumferential edge extending in the direction of the annular space, with axial bores in the edge of the ring-shaped end plate arranged downstream. The axial bores extend from the annual space into the end plate, and at least one opening is for removing cooling air, the opening branching from the axial bore.