A safety cap comprising: a screw-type inner cap detachably mounted on a mouth of a container; and an outer cap that is combined with the inner cap so as to be rotatable relative to the inner cap, each of the inner cap and the outer cap having a plurality of engaging protuberances (13, 23), the engaging protuberances of the inner cap and the engaging protuberances of the outer cap being engaged with each other and rotating the inner cap when the outer cap is rotated while being pressed toward the inner cap, each of the engaging protuberances (13, 23) having a vertical part that is engaged when the outer cap is rotated in a closing direction and an inclined part that is engaged when the outer cap is rotated in an opening direction, and the inclined part having a steeply inclined part (13b, 23b) that has a steep inclination and a gently inclined part (13b1, 23b1) that has a gentler inclination than the steeply inclined part (13b, 23b), the steeply inclined part (13b, 23b) and the gently inclined part (13b1, 23b1) being continuous with each other, wherein the inclined part has a convex inclined part that is formed into a convex shape by the steeply inclined part (13b, 23b) and the gently inclined part (13b1, 23b1) in one of the engaging protuberance of the inner cap and the engaging protuberance of the outer cap and a concave inclined part that is formed into a concave shape by the steeply inclined part (13b, 23b) and the gently inclined part (13b1, 23b1) in the other of the engaging protuberance of the inner cap and the engaging protuberance of the outer cap, and characterised in that the convex inclined part and the concave inclined part are engage-able in close contact with each other. a screw-type inner cap detachably mounted on a mouth of a container; and an outer cap that is combined with the inner cap so as to be rotatable relative to the inner cap, each of the inner cap and the outer cap having a plurality of engaging protuberances (13, 23), the engaging protuberances of the inner cap and the engaging protuberances of the outer cap being engaged with each other and rotating the inner cap when the outer cap is rotated while being pressed toward the inner cap, each of the engaging protuberances (13, 23) having a vertical part that is engaged when the outer cap is rotated in a closing direction and an inclined part that is engaged when the outer cap is rotated in an opening direction, and the inclined part having a steeply inclined part (13b, 23b) that has a steep inclination and a gently inclined part (13b1, 23b1) that has a gentler inclination than the steeply inclined part (13b, 23b), the steeply inclined part (13b, 23b) and the gently inclined part (13b1, 23b1) being continuous with each other, wherein the inclined part has a convex inclined part that is formed into a convex shape by the steeply inclined part (13b, 23b) and the gently inclined part (13b1, 23b1) in one of the engaging protuberance of the inner cap and the engaging protuberance of the outer cap and a concave inclined part that is formed into a concave shape by the steeply inclined part (13b, 23b) and the gently inclined part (13b1, 23b1) in the other of the engaging protuberance of the inner cap and the engaging protuberance of the outer cap, and characterised in that the convex inclined part and the concave inclined part are engage-able in close contact with each other.