We report results of inelastic-neutron-scattering measurements of low-energy spin-wave excitations in two structurally distinct families of iron-pnictide parent compounds: Na1-delta FeAs and BaFe2As2. Despite their very different values of the ordered magnetic moment and Neel temperatures, T-N, in the antiferromagnetic state both compounds exhibit similar spin gaps of the order of 10 meV at the magnetic Brillouin-zone center. The gap opens sharply below T-N, with no signatures of a precursor gap at temperatures between the orthorhombic and magnetic phase transitions in Na1-delta FeAs. We also find a relatively weak dispersion of the spin-wave gap in BaFe2As2 along the out-of-plane momentum component, q(z). At the magnetic zone boundary (q(z) = 0), spin excitations in the ordered state persist down to similar to 20 meV, which implies a much smaller value of the effective out-of-plane exchange interaction, J(c), as compared to previous estimates based on fitting the high-energy spin-wave dispersion to a Heisenberg-type model.