The hyperfine splitting values of the ground state of the hydrogenlike atoms C5+13, N6+14, O7+17 and the lithiumlike atoms Li07, N4+14, F6+19, Na8+23, Mg9+25, Al10+27, Si11+29, Cl14+35, Fe23+57 are calculated. The calculations of the lithiumlike ions (Z7) are based on a combination of the 1/Z perturbation theory and the configuration interaction Hartree-Fock method. The relativistic corrections are calculated in the zeroth and first orders in 1/Z. The nuclear charge and magnetization distribution corrections and the radiative corrections are taken into account. The uncertainty of the calculations is estimated to be ∼0.02% for the hydrogenlike ions and ∼0.06% for the lithiumlike ions, except Fe23+57, for which the uncertainty is about 0.15%. The hyperfine structure constant of the ground state of Li is calculated to be A=401.5(4) MHz. The results of the calculations are compared with the theoretical values obtained with other methods and with experiment.