  This paper gives conditions for the rightmost particle in the $n$th
generation of a multitype branching random walk to have a speed, in the sense
that its location divided by n converges to a constant as n goes to infinity.
Furthermore, a formula for the speed is obtained in terms of the reproduction
laws. The case where the collection of types is irreducible was treated long
ago. In addition, the asymptotic behavior of the number in the nth generation
to the right of na is obtained. The initial motive for considering the
reducible case was results for a deterministic spatial population model with
several types of individual discussed by Weinberger, Lewis and Li [J. Math.
Biol. 55 (2007) 207-222]: the speed identified here for the branching random
walk corresponds to an upper bound for the speed identified there for the
deterministic model.
