A reheat combustion system for a gas turbine comprises a mixing tube adapted to be fed by products of a primary combustion zone of the gas turbine and by fuel injected by a lance; a combustion chamber fed by the said mixing tube; and at least one perforated acoustic screen. The or each said acoustic screen is provided inside the mixing tube or the combustion chamber, at a position where it faces, but is spaced from, a perforated wall thereof. In use, the perforated wall experiences impingement cooling as it admits air into the combustion system for onward passage through the perforations of the said acoustic screen, and the acoustic screen damps acoustic pulsations in the mixing tube and combustion chamber.