The stability and nonlinear interaction between the disturbances in a round jet are investigated numerically at Re = 2850. The conditions of the laboratory experiment performed earlier in the Institute of Mechanics of Moscow State University are reproduced. The characteristic feature of the jet considered is the presence of three points of inflection in the inflow velocity profile. This fact determines essentially the properties of flow. Linear stability is investigated using two approaches: quasi-parallel and spatial. Good quantitative agreement between the results of two approaches and adequate agreement with the results of inviscid theory are obtained. Numerical calculations are carried out with the aim to explain and interpret the results of the laboratory experiment in which change in the length of the laminar-turbulent transition zone in the jet under the action of time-periodic axisymmetric perturbations is revealed. It is shown that axisymmetric disturbances of even considerable initial amplitude do not lead to laminar-turbulent transition. The transition observed experimentally is attributable to the presence of non-controlled three-dimensional disturbances that are strengthened against the background of fairly intense artificial disturbances. The investigations carried out in the present study confirm this hypothesis. Thus, the three-dimensional disturbances serve as an initiator of transition, while the axisymmetric disturbances of a fairly high amplitude only accelerate their growth. It is shown that more intense three-dimensional disturbances are able to ensure still more rapid transition even in the absence of axisymmetric component.