This thesis is a study into the response and seismic safety of three-dimensional multi-storey concrete structures under concurrent orthogonal seismic excitations. It employs the nonlinear time-history method as its analysis tools. Time-history analyses rely heavily on their utilised earthquake records. Accordingly, this study examines the different approaches of selecting earthquake suites and develops a methodology of selecting representative earthquake scenarios. This methodology is credibly implemented in selecting a far- and a near field suites representative of the New Zealand seismic hazard. The study investigates the response of 6-, 9- and 12-storey concrete structures of different n-X-bays × m-Y-bays. Bidirectional responses of these considered structures are examined and consequently the current combination rules are scrutinised. Consequently this study strongly recommends the use of the 40-percent combination rule in lieu of the widely used 30-percent rule; and the use of time-history analysis in lieu of quasi/equivalent static and response modal analysis methods to avoid their strong dependence on combination rules. An intensive study is conducted employing the incremental dynamic analysis (IDA) technique to investigate structural demands of interstorey drifts, lateral storey drifts and storey accelerations. The study utilises the developed far-field suite and identifies the 50th and 90th percentile demands. Hence it provides easy-to-use expressions to facilitate rapid calculation of the structural demands and the effects of biaxial interactions. An implementation into the Demand and Capacity Factor Design (DCFD) format is presented that infers confidence in the performance levels of the considered structures. The study also draws attention to the importance of considering storey accelerations as their storey values reach as high as 10 × PGA. A sensitivity study is conducted by repeating the IDA investigation while using the developed near-field suite. Subsequently a comparison between the near- and the far-field results is conducted. The results were markedly similar albeit of less magnitudes until the (seismic hazard) intensity measure IM = Sa(T₁) = 0.4g when the near-field results show sudden flat large increase in demands suggesting a brittle collapse. This is attributed to the higher content of the higher mode frequencies contained in near-field ground motions. Finally, the study examines the (vectorial) radial horizontal shear demands in columns and beam-column joints of the previous far- and near-field studies. The combined radial shear demands in corner, edge and internal columns and joints are evaluated that roughly show a square-root proportional relationship with IM that exhibit somewhat brittle failure at IM ≥ 0.35g. Shears demands in the (4-way) internal columns and the (2-way) corner joints show highest magnitude in their respective class. The results suggest transverse joint shear reinforcement of 1.5, 1.0 and 0.5 of the longitudinal reinforcement of the neighbouring beam respectively for corner, edge and internal joints. An implementation of a proposed practical (and simpler) DCFD format shows satisfactory confidence in columns performance in shear up to IM = 0.35g, conversely to joints unsatisfactory performance in shear at the onset of inelastic behaviour (IM > 0.05g).