A catalyst composition consisting essentially of(A) a crystalline aluminosilicate zeolite having a silica/alumina mole ratio of at least 10, at least 50% of all its cation sites bing occupied by an alkali metal cation (component A), and(B) a refractory inorganic oxide having (b-1) platinum and (b-2) tin and/or indium supported thereon (component B). A process for cracking non-aromatic hydrocarbons in the presence of the catalyst composition, and a process for isomerizing C.sub.8 aromatic hydrocarbons, particularly xylenes, by applying the catalyst composition in combination with a conventional isomerization catalyst.