NOVELTY - Oligomeric compounds of the D-glucuronic acid or D-glucuronate with beta (1-4) sequence (I).    USE - (I) is useful for stimulating the elasticity of the dermis and epidermis, reinforcing the dermal-epidermal cohesion to fight against skin aging, fine lines, wrinkles, visible discontinuities and/or tactile skin, loss of firmness, elasticity and tone and deformability of skin tissue, where: (I) reinforces the elastic properties of the skin by promoting the stimulation of the synthesis of hyaluronic acid and/or CD44 receptor expression in keratinocytes; (I) enhances the elasticity of the skin by promoting the synthesis of elastin and preserving the dermal protein with long life of glycation; and (I) stabilize and strengthen the dermo-epidermal stimulation by promoting the synthesis of laminin. (I) is useful for moisturizing the skin and fighting against water loss in the skin. (I) is useful for treating wrinkles and fine lines, and strengthening skin elasticity and dermal-epidermal properties. The composition is useful in the form of galenic creams or lotions, ointment milks or creams, gels, emulsions, dispersions, solutions, suspensions, cleansers, foundations, anhydrous preparations (sticks, preferably lip balm, body oils and bath oils ), shower gels and bath products, lotions and shampoos for hair care, milks or creams for skin or hair care, lotions or milks cleansers, sunscreen lotions, milks or creams, lotions, milks or creams of artificial tanning, shaving creams or foams, aftershave lotions, lipsticks, mascaras or nail polish, essence of skin serums, adhesive materials or absorbents, transdermal patches, or powders. The composition is useful to defuse, relax and smooth the skin (all claimed). The anti-aging effect of (I) was tested in human skin. The result showed that, after treatment with steroids, a decrease in the amount of laminin at the dermo-epidermal with a score of 1.28 versus 2.2 for skin control was observed, and after treatment with 9.1% acetylated oligoglucuronane, significant expression of laminin with a score of 2.2 versus 1.28 for the aged skin was observed.    ADVANTAGE - The preparation of (I) uses green chemistry that contributes to the preservation of the environment by consuming minimal power and rejecting little waste. The acetylated oligoglucuronanes are easily biodegradable, non-bioaccumulative and non-ecotoxic.    DETAILED DESCRIPTION - Oligomeric compounds of the D-glucuronic acid or D-glucuronate with beta (1-4) sequence of formula (I), where each cycle of glucuronic acid of (I) has a degree of acetylation of 8.7 plus minus 0.5-9.2 plus minus 0.5 wt.% of O-CO-CH3 by weight of the glucuronic acid cycle and a degree of polymerization of 18-19 plus minus 2.    R = H or COCH3, where n is not defined.    An INDEPENDENT CLAIM is included for a composition comprising at least one acetylated oligoglucuronane (I) in a medium.