Apparatus for multi- or hyperspectral imaging, comprising an illumination device for generating spectrum-addressable multi- or hyperspectral illumination light; an image capturing device configured to acquire a time sequence of two two-dimensional images of an object illuminated with the multispectral light, comprising at least one screened, two-dimensional detector having a plurality of detector elements, which is configured to detect the intensity of at least part of the light (28; 70) coming from the object; an image evaluation device configured to determine the proportions of the individual spectral components by analyzing the temporal variation of the intensity detected by each detector element and to create, based on the determined proportions of the individual spectral components, a multi- or hyperspectral image (36, 38) of the object, wherein the illumination apparatus comprises: a multispectral light source; a modulation device configured to temporally modulate the individual spectral components of the multispectral light source with mutually different modulation frequencies, modulation frequency ranges or modulation sequences, wherein (i) the multispectral light source comprises at least one light source with a continuous, quasi-continuous or frequency comb spectrum and wavelength dispersion means for spectrally dividing the light emitted by the light source into a plurality of spectral components spatially separated from one another with mutually different wavelengths λ 1, λ 2,..., λ n or wavelength bands, and the modulation device comprises at least one electrically controllable, spatial light modulator configured to temporally modulate the individual spectral components; or (ii) the multispectral light source comprises at least one set or array of monochromatic or quasi-monochromatic light sources for emitting light with mutually different emission wavelengths λ 1, λ 2,..., λ n or emission wavelength bands; and the modulation device comprises a plurality of electronic control modules associated with the individual monochromatic or quasi-monochromatic light sources, which modules are configured to time-modulate the light emitted by the respective monochromatic or quasi-monochromatic light source; and wherein the illumination apparatus further comprises optical means which are configured to combine the individual modulated spectral components of the multispectral light source so that they overlap one another substantially spatially to form the spectrum-addressable multi- or hyperspectral illumination light, characterized in that the modulation apparatus is configured to set the start phases of the modulations of the individual spectral components to be constantly decreasing or constantly increasing in relation to a start time of illumination of the screened detector. an illumination device for generating spectrum-addressable multi- or hyperspectral illumination light; an image capturing device configured to acquire a time sequence of two two-dimensional images of an object illuminated with the multispectral light, comprising at least one screened, two-dimensional detector having a plurality of detector elements, which is configured to detect the intensity of at least part of the light (28; 70) coming from the object; an image evaluation device configured to determine the proportions of the individual spectral components by analyzing the temporal variation of the intensity detected by each detector element and to create, based on the determined proportions of the individual spectral components, a multi- or hyperspectral image (36, 38) of the object, a multispectral light source; a modulation device configured to temporally modulate the individual spectral components of the multispectral light source with mutually different modulation frequencies, modulation frequency ranges or modulation sequences, (i) the multispectral light source comprises at least one light source with a continuous, quasi-continuous or frequency comb spectrum and wavelength dispersion means for spectrally dividing the light emitted by the light source into a plurality of spectral components spatially separated from one another with mutually different wavelengths λ 1, λ 2,..., λ n or wavelength bands, and the modulation device comprises at least one electrically controllable, spatial light modulator configured to temporally modulate the individual spectral components; or (ii) the multispectral light source comprises at least one set or array of monochromatic or quasi-monochromatic light sources for emitting light with mutually different emission wavelengths λ 1, λ 2,..., λ n or emission wavelength bands; and the modulation device comprises a plurality of electronic control modules associated with the individual monochromatic or quasi-monochromatic light sources, which modules are configured to time-modulate the light emitted by the respective monochromatic or quasi-monochromatic light source; and the illumination apparatus further comprises optical means which are configured to combine the individual modulated spectral components of the multispectral light source so that they overlap one another substantially spatially to form the spectrum-addressable multi- or hyperspectral illumination light, characterized in that the modulation apparatus is configured to set the start phases of the modulations of the individual spectral components to be constantly decreasing or constantly increasing in relation to a start time of illumination of the screened detector.