The maneuvering of powered two-wheelers (PTWs) is non-lane-based, and the interactions between PTWs and other vehicles in mixed traffic are complex. The behavior of PTWs, particularly in developing countries, is not the same as that of passenger cars, which has been studied for several decades. This study contributes to the existing literature on PTWs in several ways. A real-world microscopic vehicle trajectory database has been digitalized from a video clip for a four-lane urban arterial in Taipei (Taiwan). From a modeling perspective, a dynamic discrete choice model is proposed to capture the lateral-shifting behaviors of PTWs in mixed traffic conditions. The model considers not only the positions of all surrounding vehicles but also riders’ perception of expected traffic conditions. The behavioral model is able to describe the sequential non-lane-based maneuvers of PTWs, including not following lane discipline, filtering, moving abreast of other vehicles in the same lane, oblique following, swerving, and overtaking from the same lane. The results indicate that a better model fit is obtained when taking into account the dynamic nature of the problem. The data and methods proposed have the potential to improve microscopic traffic simulation of mixed traffic with a large amount of PTWs. Practical applications are concerned with the improvement of road geometries and the definition of control strategies for mixed traffic flows.