The hyperfine-structure constants of the lowest s and p_1/2 states of superheavy elements E113 and E114⁺ are presented in this article. The relativistic Hartree-Fock method with the core polarization being taken into account by means of the many-body perturbation theory. Breit and quantum electrodynamic (QED) effects are also considered. Similar calculations for Tl and Pb⁺ are used to gauge the accuracy of the calculations.