In this paper, we examine the parallel implementation
of the iterated continuous extensions (ICEs) of Baker & Paul.
We indicate how to construct arbitrarily high-order ICEs, and discuss some
of the strategies for choosing the `free' parameters of the methods. The
numerical results that we present suggest that ICEs implemented in parallel
provide an easy and efficient way of writing dense-output ordinary differential
equation codes and delay differential equation codes, even in the case
that the lag vanishes and/or is state-dependent.