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A series of monohydrides of Ru^II of formula RuH(Tp^R)(cod) 1–3 have been synthesized from the reaction of [RuH(NH₂NMe₂)₃(cod)]BPh₄ with the corresponding Tp^R ligand {hydrotris(7-methylindazol-2-yl)borate, Tp^Bo,7Me, 1; hydrotris[3-(2-thienyl)pyrazol-1-yl]borate, Tp^Tn, 2; tris[3-(2,4-dimethoxyphenyl)pyrazol-1-yl]hydroborate, Tp^{(2,4(OMe)₂Ph)}, 3}. In these compounds the Tp ligand is κ³ N,N',BH coordinated with a B–H  · · ·  Ru agostic interaction. Reactions of 1 and 2 with two-electron donor ligands, L = PMe₃, PMe₂Ph and CN-t-Bu, led to the formation of complexes of formula RuH(Tp^R)(L)(cod) (Tp^R = Tp^Bo,7Me, L = PMe₃ 4, PMe₂Ph 5 or CN-t-Bu 6; Tp^R = Tp^Tn, L = PMe₃ 7, PMe₂Ph 8 or CN-t-Bu, 9). In this new series the incoming ligands replace one of the coordinated pyrazole rings instead of the stated B–H  · · ·  Ru interaction which remains and consequently the Tp^R ligands are κ² N,BH coordinated. The molecular structure of 7 was determined by an X-ray diffraction study. The ruthenium atom has a distorted octahedral environment with the ligand Tp^Tn coordinated through only one pyrazole ring and an agostic B–H group. The two hydrides are in a mutually trans disposition with an angle of 166°. The Ru  · · ·  H distance is 2.07(5) and Ru–H_terminal 1.33(5) Å. The molecular structure of the model complex [RuH(κ²-N,BH-Tp)(PH₃)(H₂C&z.dbd6;CH₂)₂] has been optimised with the aid of ab initio calculations in order to compare the structural parameters with those of the experimentally determined structure.