A composition comprising a lactone-modified alicyclic compound (I), or an epoxidized lactone-modified alicyclic compound (II) of the following formulae: ##STR1## wherein R is an alkyl group, an aromatic group or an alkenyl group having carbon number of from 1 to 30, Y.sup.1 is at least one of the structural groups; ##STR2## Y.sup.2 is at least one of the structural group; ##STR3## X is the structural group; ##STR4## R.sup.4 and R.sup.b each independently is hydrogen or a methyl group, c and c' represent a number of from 4 to 8, from n1 to nL represents 0 or a number of more than 0, respectively, and n1+n2+n3+. . . +nL corresponds to the total mole numbers of a lactone introduced into one molecule.These compositions can be made into a heat-curable composition, a photo-curable composition, a polymerizable composition and another photo-curable composition.