We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa, and Jungck-Noor iterations can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations, and extensions of the work of Olatinwo and Imoru (2008), Olatinwo (2008). Consequently, several results in literature are generalized
