In this paper we propose two new classes of asymptotically
distribution-free Renyi-type tests for testing the equality of two
risks in a competing risk model with possible censoring.  This work
extends the work of Aly, Kochar and McKeague [1994, {\it Journal of
  American Statistical Association}, {\bf 89}, 994-999] and many of
the existing tests for this problem belong to these newly proposed
classes.  The asymptotic properties of the proposed tests are
investigated.  Simulation studies are done to compare the performance
with existing tests.  A competing risks data set is analyzed to
demonstrate the usefulness of the procedure.