[en] One of the urgent problems of the nuclear-magnetic logging - the detection of low-power signals of the nuclear induction against the background of the fluctuation noise is discussed. Principal sources of the noise occurring in the gauge track of nuclear-magnetic logging instruments are shown and their statistical characteristics are given. The features of the application of the statistical decision theory methods for the processing of nuclear-magnetic logging signals and areas of the using available structural schemes of the optimal processing of signals are indicated. Great attention is paid to the evaluation of potential characteristics of the detection quality. Numerical values of the detection quality are suggested for signals with the most wide-spread practicable parameters. The results are plotted