Second-order contributions of diamagnetic interaction to the energyshift and splitting are studied in the basis of the angular momentumeigenfunctions for two kinds of Rydberg states in atoms: (i)hydrogen-like degenerate states and (ii) nondegenerateRydberg states with small magnetic quantum number, m ≤ 3,in many-electron atoms. General formulae are presented forcalculations of higher order energy corrections in degenerate stateswith the use of reduced Green’s function. The analyticalexpressions are derived for the second-order radial matrix elements ofoperator r2 and for the second-order diamagneticsusceptibilities of hydrogen-like states with m ≥ n-5. The quasiclassical quantum defect methodis used to calculate the irreducible componentsβnl(p) of the diamagneticsusceptibility χnlm(2) for Rydbergstates of alkali atoms. The numerical results are presented forsusceptibilities of degenerate hydrogen substates, and forsusceptibilities of alkali atoms in Rydberg s-, p-, d-states. Theasymptotic dependence of susceptibilities in alkali atoms on theeffective principal quantum number ν is determined numerically andthe deviation from that of the hydrogen-like states is discovered. Thedata is also presented for the scaling parameterscl(p), determining theirreducible parts of the diamagnetic susceptibilities in states withhigh ν, according to the asymptotic formulaβnl(p) = cl(p)ν11.