Proton therapy offers low integral dose and good tumor comformality in many deep-seated tumors. However, secondary particles generated during proton therapy, such as neutrons, are a concern, especially for passive scattering systems. In this type of system, the proton beam interacts with several components of the treatment nozzle that lie along the delivery path and can produce secondary neutrons. Neutron production along the beam's central axis in a double scattering passive system was examined using Monte Carlo simulations. Neutron fluence and energy distribution were determined downstream of the nozzle's major components at different radial distances from the central axis. In addition, the neutron absorbed dose per primary proton around the nozzle was investigated. Neutron fluence was highest immediately downstream of the range modulator wheel (RMW) but decreased as distance from the RMW increased. The nozzle's final collimator and snout also contributed to the production of high-energy neutrons. In fact, for the smallest treatment volume simulated, the neutron absorbed dose per proton at isocenter increased by a factor of 20 due to the snout presence when compared with a nozzle without a snout. The presented results can be used to design more effective local shielding components inside the treatment nozzle as well as to better understand the treatment room shielding requirements.