Geometries, inversion barriers, static and dynamic electronic and vibrational dipole polarizability (R), and first (beta) and second (gamma) hyperpolarizability of the pyrrole homologues C4H4XH (X = N, P, As, Sb, Bi) have been calculated by Hartree-Fock, Moller-Plesset second-order perturbation theory, coupled-cluster theory accounting for singles, doubles, and noniterative triple excitations methods, as well as density functional theory using B3LYP and PBE1PBE functionals and Sadlej's Pol and 6-311G** basis sets. Relativistic effects on the heavier homologues stibole and bismole have been taken into account within effective core potential approximation. The results show that the electronic (hyper) polarizabilities monotonically increase with the atomic number of the heteroatom, consistent with the decrease in the molecular hardness. Ring planarization reduces the carbon-carbon bond length alternation of the cis-butadienic unit, enhancing the electronic polarizability values () by 4-12% and the (hyper) polarizability values (beta(e)(vec) and ) by 30-90%. Pure vibrational and zero-point vibrational average contributions to the (hyper) polarizabilities have been determined within the clamped nucleus approach. In the static limit, the pure vibrational hyperpolarizabilities have a major contribution. Anharmonic corrections dominate the pure vibrational hyperpolarizabilities of pyrrole, while they are less important for the heavier homologues. Static and dynamic electronic response properties of the pyrrole homologues are comparable to or larger than the corresponding properties of the furan and cyclopentadiene homologue series.