RUBBER COMPOSITION AND CROSSLINKED RUBBER COMPOSITION

A rubber composition, comprising:an uncross-linked rubber having no hydrogen-bond cross-linkable moiety; andat least one polymer component selected from the group consisting of polymers (A) each of which has a side chain (a) containing a hydrogen-bond cross-linkable moiety having a carbonyl-containing group and/or a nitrogen-containing heterocycle and has a glass-transition point of 25°C or below and polymers (B) each of which contains a hydrogen-bond cross-linkable moiety and a covalent-bond cross-linking moiety in a side chain and has a glass-transition point of 25°C or below; whereinan amount of the polymer component contained is 0.01 to 200 parts by mass relative to 100 parts by mass of the uncross-linked rubber, andthe polymers (A) and the polymers (B) are each a reaction product of a maleic anhydride graft-modified thermoplastic polymer having a maleation ratio of 0.1 to 10% by mass and a cross-linkable compound.