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A spherical microphone array is presented which incorporates multiple nulls in the beampattern for analysis of directional room impulse responses. Improved performance is achieved compared to spherical arrays with regular beampatterns due to the ability to attenuate undesired room reflections. Formulation of the multiple-null spherical array processing is presented, both in the space and spherical harmonics domains. The paper concludes with experimental investigation using impulse response data measured in an auditorium.