  We study direct products of free-abelian and free groups with special
emphasis on algorithmic problems. After giving natural extensions of standard
notions into that family, we find an explicit expression for an arbitrary
endomorphism of $\ZZ^m \times F_n$. These tools are used to solve several
algorithmic and decision problems for $\ZZ^m \times F_n $: the membership
problem, the isomorphism problem, the finite index problem, the subgroup and
coset intersection problems, the fixed point problem, and the Whitehead
problem.
