Recent rapid development of industrial usage of carbon nanotubes (CNTs) has raised health concerns as these engineered elongated particles resemble the appearance of asbestos, which is a well-known inhalation hazard. While CNTs have elongated rod shaped structure similar to asbestos, they are nanosized, and therefore, their motions are strongly affected by Brownian diffusion. The available studies in this area are rather limited and details of the nanofiber dynamics along the transport route are largely unknown. In this study, the CNTs were modeled as elongated ellipsoids and their full motions including the coupled translational and rotational movement in the human tracheobronchial first airway bifurcation were analyzed. Particular attention was given to the effects of the slip-correction and Brownian motion, which are critical to the accuracy of the modeling of motions of nanoscale CNTs in free molecular and transition regimes.