  Quantum operations are used to describe the observed probability
distributions and conditional states of the measured system. In this paper, we
address the problem of their joint measurability (coexistence). We derive two
equivalent coexistence criteria. The two most common classes of operations -
Luders operations and conditional state preparators - are analyzed. It is shown
that Luders operations are coexistent only under very restrictive conditions,
when the associated effects are either proportional to each other, or disjoint.
