**Abstract:**
Hidden quantum Markovian models are generalizations of classical ones,
where the space of of classical states one uses quantum states. This
topic can have many applications, e.g. improvement a DNA analysis when
quantum effects may play role. The idea is nevertheless new, hence we
will discuss only basic results about structure of these models and
their consistency as such - nothing of that type is known so far. In
the second part we will discuss the question whether a quantum measurement
can predict what a person will do in the future. We can present a proof
it cannot based on the assumption of a unique unitary evolution.