Investigation made by powder X-ray diffraction, susceptibility measurement and powder neutron diffraction on the new TiNiSi-type (S.G. Pnma) TbMnSi, DyMnSi and NdMnGe compounds in a high-temperature form are reported. All three compounds are antiferromagnetic below T-N = 410, 400 and 430 K, respectively. Between T-N and T-t (<150 K), their magnetic structures are collinear antiferromagnetic, with Mn moments aligned along [100] in the case of TbMnSi and DyMnSi and COO II in the case of NdMnGe. Below T-t, flat spiral structures characterized by a (q(x), 0, 0) wave vector and the Mn and R (Tb, Dy and Nd) moments lying in the (0 0 I) plane take place. At 2 K, the values of the magnetic moments are: mu(Mn) = 3.30 (5) mu(B), mu(Tb) = 8.63 (5) mu(B); mu(Mn) = 3.2 (1) mu(B), mu(Dy) = 9.1(2) mu(B) and mu(Mn) = 3.73 (10) mu(B), mu(Nd) = 3.30 (8) mu(B) for TbMnSi, DyMnSi and NdMnGe, respectively. In the whole ordered range, the magnetic structures are characterized by antiferromagnetic Mn-Mn [010] zig-zag chains. The results are discussed and compared with those previously obtained on the corresponding CeFeSi-type (S.G. P4/nmm) TbMnSi and NdMnGe compounds. The Mn sublattice magnetic behaviour is also examined in the whole TiNiSi-type ternary silicides and germanides series. (C) 1999 Elsevier Science B.V. All rights reserved.