We study the typing properties of CPS conversion for an extension of $\Fomega$
with control operators.  Two classes of evaluation strategies are considered,
each with call-by-name and call-by-value variants.  Under the ``standard''
strategies, constructor abstractions are values, and constructor applications
can lead to non-trivial control effects.  In contrast, the ``ML-like''
strategies evaluate beneath constructor abstractions, reflecting the usual
interpretation of programs in languages based on implicit polymorphism.  Three
continuation passing style sub-languages are considered, one on which the
standard strategies coincide, one on which the ML-like strategies coincide,
and one on which all the strategies coincide.  Compositional, type-preserving
CPS transformation algorithms are given for the standard strategies, resulting
in terms on which all evaluation strategies coincide.  This has as a corollary
the soundness and termination of well-typed programs under the standard
evaluation strategies.  A similar result is obtained for the ML-like
call-by-name strategy.  In contrast, such results are obtained for the call-by
value ML-like strategy only for a restricted sub-language in which constructor
abstractions are limited to values.