Flow behavior in bifurcation models is understandably of great importance to health risk assessments and pulmonary drug delivery. Our understanding of such flows, however, remains fairly limited; this is particularly true of secondary flow behavior in multi-bifurcation models. Secondary flows in bifurcations can play a significant role in ultra-fine aerosol transport in the lungs. Previously, both numerical and experimental methods have shown that four-vortex secondary flow structures can develop in the cross-sections of grand-daughter branches. Evolution of such secondary flows has also been shown to depend strongly on the axial velocity profile in the preceding generation. For the unsteady case, we investigate the transient response of these secondary flow structures to an unsteady oscillatory flow at the parent inlet, as well as the interactions between potentially unstable vortex structures. The results obtained may be useful in analyzing transport phenomena in human airways under high-frequency ventilation.