Abstract. Kanazawa has shown that k-valued classical categorial grammars have the property of finite elasticity [1], which is a sufficient condition for learnability. He has also partially extended his result to general combinatory grammars, but left open the question of whether some subsets of general combinatory grammars have finite elasticity. We propose a new sufficient condition which implies learnability of some classes of k-valued general combinatory grammars, focusing on the way languages are expressed through a grammatical formalism rather than the classes of languages themselves.