  We present a theory of environmental bisimilarity for the delimited-control
operators {\it shift} and {\it reset}. We consider two different notions of
contextual equivalence: one that does not require the presence of a top-level
control delimiter when executing tested terms, and another one, fully
compatible with the original CPS semantics of shift and reset, that does. For
each of them, we develop sound and complete environmental bisimilarities, and
we discuss up-to techniques.
