  In the present paper, we introduce so-called operator-stable-like processes.
Roughly speaking, they behave locally like operator-stable processes, but they
need not to be homogenous in space. Having shown existence for this class of
processes, we analyze maximal estimates, the existence of moments, the short-
and long-time behavior of the sample paths and $p$-variation. The class
introduced here includes stable-like processes as special case.
