The laminar flow in the small bronchial tubes is quite complex due to the presence of vortex-dominated, secondary flows. Contributing to this complexity are the geometrical characteristics of the bronchial tubes that include asymmetric and nonplanar branching. These secondary flow fields play a crucial role in particle deposition; however, the actual mechanisms that determine the particle distributions are not fully understood. The research reported here increases understanding of this phenomenon by studying flow structure/ particle interaction in the small bronchial tubes for steady and unsteady respiratory conditions. Specifically, the effects of simultaneous nonplanar and asymmetric branching were investigated. The nonplanar model was generated by applying a 90◦ out-of-plane rotation to the third-generation branches. Steady-state inspiratory flows for a Reynolds number of 1,000 and unsteady periodic flows with a 30-respiration-per-minute breathing frequency were simulated in three-generation, asymmetric, planar and nonplanar models. The asymmetry and nonplanarity produced asymmetric secondary flow patterns and unequal mass flow partitioning in the third-generation branches. Ten micron water droplet deposition in the nonplanar model was found to be significantly different from the planar model, demonstrating the impact of simultaneous nonplanar and asymmetric branching. The unsteady nature of the flow also affected particle deposition. Particles released at the same instantaneous inflow conditions during off-peak inhalation conditions, generated significantly different particle deposition patterns. The differences were attributed to the high temporal variations of the fluid velocities at these off-peak times and history effects in the flows. It was also observed that the initial particle velocities had a significant impact on particle deposition. The study of flow structure and particle interaction was facilitated by the development of a novel visualization technique that employs finite-time Lyapunov exponents (FTLE). This research provides a better understanding of the fluid dynamics driving the particle deposition in the bronchial tubes.