Abstract: The beta decay of the neutron-rich In-134 and In-135 was investigated experimentally in order to provide new insights into the nuclear structure of the tin isotopes with magic proton number Z = 50 above the N = 82 shell. The beta-delayed gamma-ray spectroscopy measurement was performed at the ISOLDE facility at CERN, where indium isotopes were selectively laser-ionized and on-line mass separated. Three beta-decay branches of In-134 were established, two of which were observed for the first time. Population of neutron-unbound states decaying via gamma rays was identified in the two daughter nuclei of In-134, Sn-134 and Sn-133, at excitation energies exceeding the neutron separation energy by 1 MeV. The beta-delayed one-and two-neutron emission branching ratios of In-134 were determined and compared with theoretical calculations. The beta-delayed one-neutron decay was observed to be dominant beta-decay branch of In-134 even though the Gamow-Teller resonance is located substantially above the two-neutron separation energy of Sn-134. Transitions following the beta decay of In-135 are reported for the first time, including gamma rays tentatively attributed to Sn-135. In total, six new levels were identified in Sn-134 on the basis of the beta gamma gamma coincidences observed in the In-134 and In-135 beta decays. A transition that might be a candidate for deexciting the missing neutron single-particle 13/2(+) state in Sn-133 was observed in both beta decays and its assignment is discussed. Experimental level schemes of Sn-134 and Sn-135 are compared with shell-model predictions. Using the fast timing technique, half-lives of the 2(+), 4(+), and 6(+) levels in Sn-134 were determined. From the lifetime of the 4(+) state measured for the first time, an unexpectedly large B(E2; 4(+) -> 2(+)) transition strength was deduced, which is not reproduced by the shell-model calculations.