A one-part polysiloxane composition comprising a branched organopolysiloxane with vinyl groups bonded to silicon atoms, an organohydrogenpolysiloxane with at least two hydrogen atoms bonded to molecular chain terminal silicon atoms within each molecule, and a platinum based catalyst, together with an additional phosphite triester and an organic peroxide, is resistant to increases in viscosity, and does not gel, even on extended storage at room temperature. Even after storage, the characteristics of the cured gel product are unchanged. Accordingly, a composition of the present invention offers excellent long term storage stability at room temperature.