The early stages of laminar-turbulent transition in stenotic flows is studied by solving the full Navier-Stokes equations in cylindrical coordinates. For the linear stability analysis and the fully nonlinear direct numerical simulations, both steady and unsteady inflow velocity profiles are considered. The initial linear growth of small three-dimensional disturbances in axisymmetric stenotic basic flows for different Reynolds numbers and degrees of stenosis is investigated by considering the linearized Navier-Stokes equations in disturbance flow formulation. By introducing pulse disturbances different types of instability mechanisms can be analyzed such as biglobal instabilities, transient growth, and convective wave-like instabilities. All three types of instability mechanisms have been found to be relevant for the transition process in stenotic flows. Furthermore, nonlinear direct numerical simulations are employed to investigate which of the different instability mechanisms identified in the linear stability analysis are most relevant for the transition process.