  We show that the conjugacy problem is solvable in [finitely generated
free]-by-cyclic groups, by using a result of O. Maslakova that one can
algorithmically find generating sets for the fixed subgroups of free group
automorphisms, and one of P. Brinkmann that one can determine whether two
cyclic words in a free group are mapped to each other by some power of a given
automorphism. The algorithm effectively computes a conjugating element, if it
exists. We also solve the power conjugacy problem and give an algorithm to
recognize if two given elements of a finitely generated free group are
Reidemeister equivalent with respect to a given automorphism.
