  We consider probabilistic systems with hidden state and unobservable
transitions, an extension of Hidden Markov Models (HMMs) that in particular
admits unobservable {\epsilon}-transitions (also called null transitions),
allowing state changes of which the observer is unaware. Due to the presence of
{\epsilon}-loops this additional feature complicates the theory and requires to
carefully set up the corresponding probability space and random variables. In
particular we present an algorithm for determining the most probable
explanation given an observation (a generalization of the Viterbi algorithm for
HMMs) and a method for parameter learning that adapts the probabilities of a
given model based on an observation (a generalization of the Baum-Welch
algorithm). The latter algorithm guarantees that the given observation has a
higher (or equal) probability after adjustment of the parameters and its
correctness can be derived directly from the so-called EM algorithm.
