To enhance the quality of speech in a hands--free telecommunication environment, microphone arrays consisting of multiple microphones can be used for sound pick--up. To circumvent the limitations associated with small array apertures adaptive signal processing techniques can be used. For extreme situations of a free (coherent) and a diffuse (incoherent) noise field, acceptable solutions for the noise reduction problem exist: In coherent noise fields, the adaptive beamforming techniques yield a high-noise reduction performance, but loose their efficiency in incoherent noise fields. On the other hand, for incoherent noise fields microphone arrays with adaptive post--filtering yield good performance; but in a coherent noise environment this method may cause unacceptable distortions in the output signal. In this contribution the advantages and disadvantages of these two techniques for noise reduction are discussed. A technique is presented which operates independently of the correlation properties of the noise fields, i.e., this method is able to reduce coherent and incoherent noise simultaneously. Some results are given using objective quality measures as well as subjective listening tests. The methods are also compared by using the recognition rate of a speaker-independent isolated word recognition system.