Abstract: In a method and apparatus for the production of a nuclear magnetic resonance (NMR) tomography image with radio frequency (RF) signals from an extended measuring object (11) being detected by n surface coils (2a, 2b, 2c, 2d) of an NMR apparatus, whereby n>1, and the n RF signals are separately preamplified by n preamplifiers (3a, 3b, 3c, 3d) each assigned to one of the n surface coils (2a, 2b, 2c, 2d), and subsequently further amplified and detected in a phase sensitive fashion, as a result of which a low frequency signal is obtained in each case which is introduced to one of n low pass filters (5a, 5b, 5c, 5d) of an analog/digital converter (ADC) and whereby n partial images are produced in a computer (8) from the n signals obtained in this fashion and assembled into a single NMR tomography image of the measuring object (11) in a region of interest, the signals emanating from the n low pass filters (5a, 5b, 5c, 5d) are introduced to a single ADC (7) via a first multiplexing circuit (6) to be digitized and