In previous efforts mathematical models have been developed (Balásházy et al., 1990a, b) to describe behavior of compact particles at airway bifurcations under the simultaneous action of inertial impactional and gravitational deposition mechanisms. Now, we expand the theory for the motion of fibrous particles where another deposition process, interception, may play an important role. Current U.S. EPA health effects concerns include both natural (asbestos) and manufactured (glass) airborne fibers. For the calculation of the deposition efficiency we assume that fibers are either parallel, perpendicular, or randomly oriented to their centers-of-mass trajectories relative to the entraining airflow. Deposition is computed using three different morphological configurations to characterize a bifurcation zone: (i) a single tube bend (Model I); (ii) a straight parent tube attached to two curved daughter tubes (Model II); and, (iii) three straight tubes joined together by two curved tube sections (Model III). A refinement of Model III is proposed to permit more accurate spatial descriptions of localized differential distributions of particle deposition efficiencies. Theoretical predictions are compared to experimental data and other computations presented in the open literature. Our calculated differential distribution patterns within bifurcation zones indicate enhanced deposition, or "hot spots", at carinal ridges. This implies increased exposures to underlying airway cells (relative to neighboring locations) which may be of importance regarding the risk assessment of inhaled fibers.