The magnetic properties of epsilon-FeSi are studied by Si-29 nuclear magnetic resonance spectra and spin-lattice relaxation, at different magnetic fields, up to 15 T. For T greater than or equal to 200 K, an asymmetric central line with a satellite-like structure is observed, having a width linearly increasing with the field and a shift proportional to the magnetic susceptibility. Below 200 K, a progressive broadening of the central line is detected on cooling, indicating an inhomogeneous distribution of local magnetization. The spin-lattice relaxation, measured across the spectrum follows a law of the form T(1)(-1)proportional to (KT)-T-2, with K corresponding to the shift of the different isocromates. The results are discussed in the light of the spin-fluctuations theory for exchange-enhanced semiconductors. (C) 2000 American Institute of Physics. [S0021-8979(00)52608-5].