Abstract: To provide more economical excitation of the laser gas in a waveguide laser comprising a resonator having a resonator axis, an optical waveguide extending with a waveguide longitudinal direction essentially in the direction of the resonator axis and a gas-discharge volume located between the optical waveguide surfaces and containing a laser gas, it is proposed that a microwave source be provided, that an overcoupling structure separate from the laser gas in the gas-discharge volume be arranged on a side of one of the optical waveguide surfaces opposite the gas-discharge volume, the overcoupling structure being connected via a waveguide to a microwave source, extending in an overcoupling direction parallel to the optical waveguide surface and bringing about in a strip region in the gas-discharge volume along the overcoupling direction a substantially constant coupling-in of the microwave power.