  We introduce the one-dimensional quasireciprocal lattices where the forward
hopping amplitudes between nearest neighboring sites $\{ t+t_{jR} \}$ are
chosen to be a random permutation of the backward hopping $\{ t+t_{jL} \}$ or
vice versa. The values of $\{ t_{jL} \}$ (or $\{t_{jR} \}$) can be periodic,
quasiperiodic, or randomly distributed. We show that the Hamiltonian matrices
are pseudo-Hermitian and the energy spectra are real as long as $\{ t_{jL} \}$
(or $\{t_{jR} \}$) are smaller than the threshold value. While the
non-Hermitian skin effect is always absent in the eigenstates due to the global
cancellation of local nonreciprocity, the competition between the
nonreciprocity and the accompanying disorders in hopping amplitudes gives rise
to energy-dependent localization transitions. Moreover, in the quasireciprocal
Su-Schrieffer-Heeger models with staggered hopping $t_{jL}$ (or $t_{jR}$),
topologically nontrivial phases are found in the real-spectra regimes
characterized by nonzero winding numbers. Finally, we propose an experimental
scheme to realize the quasireciprocal models in electrical circuits. Our
findings shed new light on the subtle interplay among nonreciprocity, disorder,
and topology.
