The time-reversal symmetry leads to the important consequences for many atomic and molecular systems. Particularly, this type of symmetry causes the additional degeneracy of energy levels of the systems containing odd number of particles with spin 1/2. In the EPR spectroscopy such levels are known as Kramers doublets (for the cubic double groups of symmetry there are also Kramers quartets) which causes the specific pecularities of the EPR spectra of Kramers systems. On the basis of conception of “partial time-reversal” [1] it was shown that in coordination compounds, containing the dimer magnetic clusters, the order of the spin levels can be changed. For example, in the case of magnetic dimer clusters formed by equivalent ions with spins S1 = S2 = 1/2 the inversion of spin levels with total spin S= 0 (the singlet spin state) and S = 1 (the triplet spin state) takes place. The partial time reversal, consisting in the change of spin projections signs, is not a symmetry transformation. However, if complete them with a compensating transformation changing the sign of the exchange integral, then the invariance of the Hamiltonian with respect to time-reversal operator is restored. It was found that in coordination compounds the dimer clusters Ti(III) – Ti(III), V(IV) – V(IV), VO(II) – VO(II), Ti(III) – V(IV), Ti(III) – VO(II), VO(II) – V(IV), V(III) – V(III), Cr(III) – Cr(III), V(II) – V(II), Cr(III) – V(II), Mn(III) – Mn(III), Cr(II) –Cr(II), Mn(III) – Cr(II), Fe(II) – Fe(II), Co(II) – Co(II), Ni(II) – Ni(II), Cu(II) – Cu(II), Ce(III) –Ce(III), Pr(III) – Pr(III), Nd(III) – Nd(III), Pm(III) – Pm(III), Sm(III) – Sm(III),Eu(III) – Eu(III), Tb(III) – Tb(III), Dy(III) – Dy(III), Ho(III) – Ho(III), Er(III) – Er(III), Tu(III) – Tu(III) and Yb(III) – Yb(III) have the singlet ground state, the dimmer clusters Ti(III) – Cu(II), V(IV) – Cu(II),VO(II) – Cu(II), V(III) – Ni(II), Cr(III) – Co(II), V(II) – Co(II), Mn(III) – Fe(II), Cr(II) – Fe(II), Ce(III) –Yb(III), Pr(III) – Tu(III), Nd(III) – Er(III), Pm(III) – Ho(III), Sm(III) – Dy(III) and Eu(III) – Tb(III) have the triplet ground state, while the dimer clusters Fe(III) – Fe(III), Mn(II) – Mn(II), Fe(III) – Mn(II) and Gd(III) – Gd(III) can have the singlet ground state, as well as the triplet one. The time-reversal symmetry leads also to the structural asymmetry of trihomonuclear magnetic clusters formed by ions with half-integer spin [2]. This result based on groups theory was confirmed by EPR, magnetic susceptibility and Mossbauer spectroscopy data for a large set of coordination compounds containing trihomonuclear clusters, such as [Fe3(OOCCH3)6(H2O)3]Cl·6H2O, [Fe3(RCO2)6(OH)2]·X·nH2O, [Fe6(O)2(OH)2(OOCCMe3)12·(HOOCCMe3)(THF)]·1.5C6H6,[Cr3O(OOCCH3)6(H2O)3]Cl·6H2 O, {[Cu3L(μ-OH)(μ3-HPO4)(H2O)][PF6]3·3H2O}n, Cu3(O2C16H23)6·1.2C6H12, Na9[Cu3(H2O)9(α-AsW9O32)2]·26H2O, [Cu3(cpse)3(H2O)3]·8.5H2O, Cu3(μ3- OH)(aaat)3(H2O)3][NO3]2 ·H2O (where Haaat=3-acetylamino-5-amino-1,2,4-triazole), {[Cu3- (μ3-OH)(aat)3(μ3-SO4)]·6H2O (where Haat=3-acetylamino-1,2,4-triazole), Na6[H4V6 IVO8(PO4)4{(OCH2)3CCH2OH}2]·18H2O, (CN3H6)4Na2[H4V6 IVO8(PO4)4{(OCH2)3CCH2OH}2]·14H2O and other.