in the present paper we give results to show that a fixed power of a mapping satisfying gene- ralized contraction type of condition of Pal and Maiti[4] or Das[l ] or Jaggi [2] is a contrac- tion of Banach type under some given conditions. In another seetion we generalize further the result of Sastry and Naidu [6 ] condisering two mappings on a metric space and get a result whe- re a fixed power of a composite map is a contraction under a given condition. The result is ba- sed on the idea of generalized orbit (to be introduced later) of two mappings.