A highly maneuverable aircraft with aerostatic lift consists, in particular, of a non-rigid airship (10) which can be piloted or radio-controlled; the airship (10) is sustained by helium and consists of two spindle-shaped elements side by side (11) joined by a connecting structure (12) to form a characteristic catamaran shape, without deflecting aerodynamic control surfaces as the command system consists of a set of several adjustable electric motors, each driving a variable-pitch propeller (13).