The magnetic properties of the TiNiSi-type RMnSi compounds (R Ho, Lu, Sc 0.9Lu 0.1) have been studied by magnetization and neutron diffraction measurements. In their whole ordered range. LuMnSi and Sc 0.9Lu 0.1MnSi exhibit flat spiral antiferromagnetic structures ( T N = 255 and 125 K, respectively) whereas HoMnSi displays three different magnetic regimes. Between 300 and 55 K, a collinear antiferromagnetic structure prevails while between 55 and 15 K, a canted antiferromagnetic structure, due to a non-collinear arrangement of the Ho moments, takes place. At lower temperatures, incommensurate components appear on both Mn and Ho sublattices yielding a “double-cone” magnetic arrangement. Within the three compounds, the Mn moment value, at 2 K, strongly decreases with the R size from 2.67 μ B in HoMnSi to 2.18 μ B in LuMnSi and 1.53 μ B in Sc 0.9Lu 0.1MnSi. In HoMnSi, the magnetic structure is characterized by antiferromagnetic MnMn zigzag chains aligned along [010]. In the LuMnsi and Sc 0.9Lu 0.1MnSi compounds, the angle between the Mn moment directions in a chain decreases with the lanthanide size from 121° in LuMnSi to 52° in Sc 0.9Lu 0.1MnSi. The magnetic interactions in the MnMn zigzag chains and the evolution of the Mn magnetic moment value are discussed and compared with those observed in the related CeFeSi-type RMnSi compounds.