The properties of liquid He-3 in a low-density aerogel preliminarily covered with a few monolayers of He-4 were studied by pulsed and nonlinear CW NMR techniques. It was found that an NMR frequency shift from the Larmor value exhibits a sharp increase at a magnetization tilting angle exceeding 104degrees. Nonlinear CW NMR signals related to the formation of a macroscopic region featuring homogeneous precession of the magnetization (homogeneous precession domain) were observed. The experimental results confirm that the low-temperature superfluid He-3 phase in the aerogel is analogous to the B-phase in bulk He-3 and indicate that the spin supercurrents play an important role in the spin dynamics of superfluid He-3 in aerogel. (C) 2002 MAIK "Nauka / Interperiodica".