A method for storing a one-pack addition curable silicone composition comprising the step of storing the one-pack addition curable silicone composition in a closed container made of a material having an oxygen permeability constant of up to 1×10 -12 cm 3 (STP) cm/cm 2 ·s·Pa, whereby the silicone composition develops a storage stability of at least 3 months at 25°C, wherein the one-pack addition curable silicone composition comprises as essential components: (A) 100 parts by weight of an organopolysiloxane containing at least two silicon-bonded aliphatic unsaturated hydrocarbon groups per molecule and having a kinematic viscosity of 60 to 100,000 mm 2 /s at 25°C, (B) 100 to 3,000 parts by weight of at least one heat conductive filler selected from the group consisting of metals, metal oxides, metal hydroxides, metal nitrides, metal carbides, and carbon allotropes, (C) an organohydrogenpolysiloxane containing at least two silicon-bonded hydrogen atoms (i.e., SiH groups) per molecule in such an amount that the number of SiH groups divided by the total number of aliphatic unsaturated hydrocarbon groups in component (A) is 0.5 to 5, and (D) an effective amount of a platinum group metal complex coordinated with an organophosphorus compound represented by the general formula : wherein R 1 which may be the same or different is an optionally substituted monovalent hydrocarbon group of 1 to 20 carbon atoms, and x is an integer of 0 to 3, and wherein the material having an oxygen permeability constant of up to 1×10 -12 cm 3 (STP) cm/ cm 2 .s.Pa includes polymers such as high density polyethylene HDPE, low density polyethylene LDPE, polypropylene, polystyrene, polycarbonate, polyvinyl acetate, polyethylene terephthalate, polyvinyl chloride PVC, polyvinylidene chloride PVDC, nylon, polyvinyl fluoride, polyacrylonitrile, and metal materials such as aluminum and stainless steel. (A) 100 parts by weight of an organopolysiloxane containing at least two silicon-bonded aliphatic unsaturated hydrocarbon groups per molecule and having a kinematic viscosity of 60 to 100,000 mm 2 /s at 25°C, (B) 100 to 3,000 parts by weight of at least one heat conductive filler selected from the group consisting of metals, metal oxides, metal hydroxides, metal nitrides, metal carbides, and carbon allotropes, (C) an organohydrogenpolysiloxane containing at least two silicon-bonded hydrogen atoms (i.e., SiH groups) per molecule in such an amount that the number of SiH groups divided by the total number of aliphatic unsaturated hydrocarbon groups in component (A) is 0.5 to 5, and (D) an effective amount of a platinum group metal complex coordinated with an organophosphorus compound represented by the general formula : wherein R 1 which may be the same or different is an optionally substituted monovalent hydrocarbon group of 1 to 20 carbon atoms, and x is an integer of 0 to 3, and wherein the material having an oxygen permeability constant of up to 1×10 -12 cm 3 (STP) cm/ cm 2 .s.Pa includes polymers such as high density polyethylene HDPE, low density polyethylene LDPE, polypropylene, polystyrene, polycarbonate, polyvinyl acetate, polyethylene terephthalate, polyvinyl chloride PVC, polyvinylidene chloride PVDC, nylon, polyvinyl fluoride, polyacrylonitrile, and metal materials such as aluminum and stainless steel. <EOS>