A problem of feedback stabilization is addressed for a class of uncertain nonlinear mechanical systems with n degrees of freedom and nc < n control inputs. Each system of the class has the structure of two coupled subsystems with nc and nr degrees of freedom, respectively, a prototype being an uncertain base isolated building structure with n degrees of freedom actively controlled via actuators applying forces to specific degrees of freedom of the base movement, nc < n in number. A nonlinear adaptive feedback strategy is described, which,
under appropriate assumptions on the system uncertainties, guarantees a form of practical stability of the zero state. Numerical simulations are also presented to illustrate the application of the control strategy to a base isolated building.