An illumination device, comprising: - a lamp, and - an adapter for connecting said lamp to a support, in particular a guide rail; wherein said lamp comprises: - at least a light source, - a guide rail that is integral with said light source, and - first electrical terminals extended along said guide rail and electrically coupled with said light source, wherein said guide rail is configured for a sliding connection with a slide provided with second electrical terminals, said first electrical terminals being configured for keeping a contact with said second electrical terminals at a plurality of different mutual positions between said slide and said guide rail; wherein said adapter comprises: - a slide slidingly connected to the guide rail, said slide comprising second electrical terminals arranged such as to establish a contact with said first electrical terminals in a plurality of mutual positions between said slide and said guide rail; and - a connecting portion connectable to said support; wherein said device further comprises an intermediate portion interposed between said slide and said connecting portion and defining a revolute joint between said slide and said connecting portion; wherein said intermediate portion comprises one first bushing-shaped body connected to the slide and one second bushing-shaped body connected to the connecting portion, said first and second bushing-shaped bodies (244, 246) being mutually rotatably connected in order to define said revolute joint; wherein said intermediate portion has an inner cavity extended between the slide and the connecting portion, said adapter comprising third electrical terminals arranged at said connecting portion and a plurality of conductive elements arranged in said inner cavity for electrically connecting the second electrical terminals and the third electrical terminals; wherein said conductive elements comprise electrical wires arranged between said first and second bushing-shaped bodies (244, 246) and having a suitable flexibility to bear mutual rotations therebetween; wherein said intermediate portion defines an end-of-stroke configured to limit a maximum mutual rotation between said first bushing-shaped body and said second bushing-shaped body. - a lamp, and - an adapter for connecting said lamp to a support, in particular a guide rail; wherein said lamp comprises: - at least a light source, - a guide rail that is integral with said light source, and - first electrical terminals extended along said guide rail and electrically coupled with said light source, - at least a light source, - a guide rail that is integral with said light source, and - first electrical terminals extended along said guide rail and electrically coupled with said light source, wherein said guide rail is configured for a sliding connection with a slide provided with second electrical terminals, said first electrical terminals being configured for keeping a contact with said second electrical terminals at a plurality of different mutual positions between said slide and said guide rail; wherein said adapter comprises: - a slide slidingly connected to the guide rail, said slide comprising second electrical terminals arranged such as to establish a contact with said first electrical terminals in a plurality of mutual positions between said slide and said guide rail; and - a connecting portion connectable to said support; - a slide slidingly connected to the guide rail, said slide comprising second electrical terminals arranged such as to establish a contact with said first electrical terminals in a plurality of mutual positions between said slide and said guide rail; and - a connecting portion connectable to said support; wherein said device further comprises an intermediate portion interposed between said slide and said connecting portion and defining a revolute joint between said slide and said connecting portion; wherein said intermediate portion comprises one first bushing-shaped body connected to the slide and one second bushing-shaped body connected to the connecting portion, said first and second bushing-shaped bodies (244, 246) being mutually rotatably connected in order to define said revolute joint; wherein said intermediate portion has an inner cavity extended between the slide and the connecting portion, said adapter comprising third electrical terminals arranged at said connecting portion and a plurality of conductive elements arranged in said inner cavity for electrically connecting the second electrical terminals and the third electrical terminals; wherein said conductive elements comprise electrical wires arranged between said first and second bushing-shaped bodies (244, 246) and having a suitable flexibility to bear mutual rotations therebetween; wherein said intermediate portion defines an end-of-stroke configured to limit a maximum mutual rotation between said first bushing-shaped body and said second bushing-shaped body.