The present invention relates to a method for suppressing the activity of the matrix metalloproteinases (MMPs) in the skin including the topical application of a composition, which has an effective ratio for the synergistic action related to the concentration of a hydroxamic acid, salt of the hydroxamic acid, and/or a complex thereof and the concentration of glycols, to the skin′s surface. According to partial embodiments of the present invention, the ratio of the weight percentage of the hydroxamic acid, salt of the hydroxamic acid, and/or the complex thereof with respect to the weight percentage of the glycols can be selected from a group including 1:1.4, 1:3, and 1:5 with respect to the weight of the total composition in an approximating manner. The present invention also relates to methods for preventing or reducing aging on the skin surface. The methods include the topical application of a composition, which has the effective ratio for the synergistic action related to the concentration of a hydroxamic acid, salt of the hydroxamic acid, and/or a complex thereof and the concentration of glycols, to the surface of a skin. The methods for increasing the enzymatic inhibition potential of the glycols include a step of coupling one or more glycols with the hydroxamic acid, salt of the hydroxamic acid, and/or a complex thereof in the amounts in accordance with the effective ratio for the synergistic action for forming a synergistic mixture. Enzymatic inhibition potential of the synergistic mixture is greater than the enzymatic inhibition potential of glycols or the hydroxamic in a standalone manner. The present invention also relates to anti-aging compositions for suppressing the activities of MMPs in the skin with the effective ratio of the concentration of the hydroxamic acid, salt of the hydroxamic acid, and/or a complex thereof and the concentration of glycols for the synergetic action within the above-described range. In partial embodiments of the present inventi
