Spiral bevel gears are used for developing silent power transmissions where shafts are non-parallel; moreover, they allow more freedom in allocating the drive motors to reduce the space. Bevel gears are used in different engineering fields, e.g., aerospace, terrestrial vehicles, heavy industries. For high-speed gearboxes using spiral bevel gears (SBGs) instead of straight bevel gears can allow to reduce the vibration magnitude, on the other hand the vibration is not completely suppressed and, in some circumstances, they can experience high vibration levels, teeth contact loss, and complex dynamic scenarios. The present study investigates the dynamic behavior of spiral bevel gears by means of a multi degrees of freedom (dofs) dynamical system having four dofs and involving the rotational shaft stiffness. The governing equations of motion are derived based on a nonlinear time-varying model. The nonlinearity and time dependency are due to backlash and contact phenomena arising from the meshing gear. We observed that, in some operating conditions, a contact loss with backside contact takes place. The amplitude-frequency and bifurcation diagrams of Poincaré maps are considered to analyze the vibration response of the system.