The problem of estimating trajectory tubes for nonlinear controlled dynamical systems with uncertainty in the initial data is studied. It is assumed that the dynamic system has a special structure in which the nonlinear terms are defined by quadratic forms on state coordinates and the values of uncertain initial states and admissible controls are constrained by ellipsoidal restrictions. Matrix of linear terms in the state system velocities is also not exactly known, but it belongs to the known compact in the corresponding space, i.e. the dynamics of the system is complicated by the presence of bilinear components in the right-hand sides of the system of differential equations. We solve the problem of estimating the reachable sets of nonlinear control system of this kind, the results make it possible to construction of the corresponding numerical algorithms. We solve here the problem of estimating the reachable sets of nonlinear controlled system of this kind, the results make it possible to construct the corresponding numerical algorithms.