A process for increasing the volume or body of hair or for improving the smoothness and softness of the skin comprising applying a cosmetic composition to said hair or skin in an amount effective to increase the volume or body of said hair or to improve the smoothness and softness of the skin, said cosmetic composition comprising a solution of, in water or a hydroalcoholic solution wherein the alcohol is ethanol or isopropanol, at least one polymer having 50 to 100% of repeating units of the .beta.-alanine type having the formula:
- ##STR25## and 0 to 50% of repeating units of the acrylamide type having the formula:
- ##STR26## wherein R.sub.1 represents hydrogen or a member selected from the group consisting of ##STR27## (ii) --CH.sub.2 OH, (iii) --(CH.sub.2).sub.n --CH.sub.3 wherein n is 0 or a whole number ranging from 1 to 11,
- (iv) ##STR28## wherein r' and r" each independently represent hydrogen or alkyl containing 1-3 carbon atoms,
- (v) --CHOH--COOH,
- (vi) --CH.sub.2 --SO.sub.3 Na,
- (vii) ##STR29## Cl.sup..crclbar. and
- (viii) --(CH.sub.2 --CH.sub.2 --O).sub.m H wherein m ranges from 1 to 10, and
- R.sub.2 anf R.sub.3 represents hydrogen or methyl.