  A criterion of joint ergodicity of several sequences of transformations of a
probability measure space $X$ of the form $T_{i}^{\phi_{i}(n)}$ is given for
the case where $T_{i}$ are commuting measure preserving transformations of $X$
and $\phi_{i}$ are integer valued generalized linear functions, that is, the
functions formed from conventional linear functions by an iterated use of
addition, multiplication by constants, and the greatest integer function. We
also establish a similar criterion for joint ergodicity of families of
transformations depending of a continuous parameter, as well as a condition of
joint ergodicity of sequences $T_{i}^{\phi_{i}(n)}$ along primes.
