A curable polyorganosiloxane composition is disclosed, comprising: (A) 100 parts by weight of polyorganosiloxane having at least two hydroxyl groups or hydrolyzable groups bonded to a silicon atom in the molecule thereof and having a viscosity at 25.degree. C. of 10 to 1,000,000 cSt, (B) 0 to 2,000 parts by weight of polyorganosiloxane having at least two alkenyl groups bonded to a silicon atom in the molecule thereof and having a viscosity at 25.degree. C. of 10 to 1,000,000 cSt, (C) 0.5 to 20 parts by weight of an organosilicon compound having more than 2 (on the average) hydrolyzable groups bonded to a silicon atom in the molecule thereof, (D) 0 to 10 parts by weight of a catalyst for a condensation reaction, and (E) 0.1 to 5 parts by weight of an organic peroxide, wherein at least 0.01 mol % of all organic groups bonded to a silicon atom as contained in (A) to (C) is an alkenyl group. The composition has both condensation reaction curability and ultraviolet ray curability.