A problem of feedback stabilization is addressed for a class of uncertain nonlinear mechanical systems with ${\textstyle n}$ degrees of freedom and ${\textstyle n_{c}<n}$ control inputs. Each system of the class has the structure of two coupled subsystems with ${\textstyle n_{c}}$ and ${\textstyle n_{r}}$ degrees of freedom, respectively, a prototype being an uncertain base isolated building structure with ${\textstyle n}$ degrees of freedom actively controlled via actuators applying forces to specific degrees of freedom of the base movement, ${\textstyle n_{c}<n}$ 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.