  In this work infinitely divisible cylindrical probability measures on
arbitrary Banach spaces are introduced. The class of infinitely divisible
cylindrical probability measures is described in terms of their
characteristics, a characterisation which is not known in general for
infinitely divisible Radon measures on Banach spaces. Further properties of
infinitely divisible cylindrical measures such as continuity are derived.
Moreover, the result on the classification enables us to conclude new results
on genuine Levy measures on Banach spaces.
