Pd(II) and Pt(II) chloride complexes with LL = methylcis-3,4-diamino-2,3,4,6-tetradeoxy-α-L-lyxo-hexopyranoside of the formulae [Pd(LL)Cl2] and [Pt(LL)Cl2], 1, were studied by 1H, 2H, 13C, 15N and 195Pt NMR spectroscopy. These techniques were applied for characterization of the structure and ligand exchange dynamics, in case of diastereomeric species formed from 1 in DMSO-d6, DMSO-h6 and H2O; their general formula was [Pt(LL)XY]+ (X = Cl, Y = DMSO-d6, 2a; X = DMSO-d6, Y = Cl, 2b; X = Cl, Y = DMSO-h6, 2a′; X = DMSO-h6, Y = Cl, 2b′; X = Cl, Y = H2O, 3a; X = H2O, Y = Cl, 3b). Their theoretical structures and NMR parameters, calculated at the level of DFT approach, were also presented and compared to the experimental data. The model complex [Pt(trans-diaminocyclohexane)Cl2], 4, was studied as well. To the best of our knowledge, this work is the first account dealing with the detailed analysis of structure and dynamics of ligand exchange processes in organic solvents and water, performed for a PtCl2 complex containing a diaminosugar moiety. The kinetic behavior of the studied coordination compounds suggests that some of them may be potentially active in bioassays against cancer cells. Compound 1 exhibits noticeable versatile ligand exchange possibilities in DMSO and H2O. Particularly, it undergoes solvolysis in DMSO-d6, exchanging one chloride atom and yielding two diastereomers 2a and 2b; the former, being the kinetically favored species, has the DMSO-d6 ligand syn to the N3 atom. The lyophilisate of the respective 2a + 2b mixture, earlier equilibrated in DMSO-d6, after dissolving in H2O yields only the latter isomer, which is thermodynamically favored. The solvolysis of 1 in H2O yields instantaneously two diastereomeric monoaquated species, 3a and 3b, amounting to 10% of each.