A nozzle assembly for laser beam cutting has a nozzle body shaped like a ncated cone fitting the focussed laser beam and surrounding the same. The assembly has a passage bore for the laser beam, with a nozzle sleeve concentrically surrounding the nozzle body and forming an annular gap therewith. An outlet bore is coaxial with the passage bore for a cutting gas stream from an annular gap connected to a gas source. The outlet bore is located on the workpiece side in front of the passage bore and has a diameter (D) exceeding the diameter (d) of the passage bore. In order to insure that the deflection of the gas stream from the nozzle takes place parallel to the axis of the laser beam, with a minimum of flow loss, the nozzle assembly is built so that the outlet cross section of the outlet bore is approximately the same as the transition cross section of the annular gap to the outlet bore.