Abstract: The high-spin structures and isomers of the N = 81 isotones Xe-135 and Ba-137 are investigated after multinucleon-transfer (MNT) and fusion-evaporation reactions. Both nuclei are populated (i) in Xe-136+ U-238 and (ii) Xe-136+ Pb-208 MNT reactions employing the high-resolution Advanced Gamma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA, (iii) in the Xe-136+ Pt-198 MNT reaction employing the gamma-ray array GAMMASPHERE in combination with the gas-detector array CHICO, and (iv) via a B-11+ Te-130 fusion-evaporation reaction with the HORUS gamma-ray array at the University of Cologne. The high-spin level schemes of Xe-135 and Ba-137 are considerably extended to higher energies. The 2058-keV (19/2(-)) state in Xe-135 is identified as an isomer, closing a gap in the systematics along the N = 81 isotones. Its half-life is measured to be 9.0(9) ns, corresponding to a reduced transition probability of B(E2,19/2(-) -> 15/2(-)) = 0.52(6) W.u. The experimentally deduced reduced transition probabilities of the isomeric states are compared to shell-model predictions. Latest shell-model calculations reproduce the experimental findings generally well and provide guidance to the interpretation of the new levels.