In a projection exposure method for the exposure of a radiation-sensitive substrate arranged in the region of an image surface of a projection objective with at least one image of a pattern of a mask arranged in the region of an object surface of the projection objective, laser radiation having a spectral intensity distribution I(ω) dependent on the angular frequency ω is used. The laser radiation is characterized by an aberration parameter α in accordance with: α := ∫ I ⁡ ( ω ) ⁢ ω 2 ⁢ ⅆ ω ∫ I ⁡ ( ω ) ⁢ ⅆ ω and a coherence time τ in accordance with: τ = ∫ I ⁡ ( ω ) 2 ⁢ ⅆ ω [ ∫ I ⁡ ( ω ) ⁢ ⅆ ω ] 2 The laser radiation is introduced into an illumination system for generating an illumination radiation directed onto the mask, and the pattern is imaged onto the substrate with the aid of a projection objective. The spectral intensity distribution is set so that ατ2≦0.3. The influence of temporally varying speckles on image generation can be reduced by comparison with conventional methods, without simultaneously increasing the influence of chromatic aberrations on image generation.