  Let k, r, s in the natural numbers where r \geq s \geq 2. Define f(s,r,k) to
be the smallest positive integer n such that for every coloring of the integers
in [1,n] there exist subsets S_1 and S_2 such that: (a) S_1 and S_2 are
monochromatic (but not necessarily of the same color), (b) |S_1| = s, |S_2| =
r, (c)max(S_1) < min(S_2), and (d) diam(S_1) \leq diam(S_2). We prove that the
theorems defining f(s,r,2) and f(s,r,3) admit a partial generalization in the
sense of the Erdos-Ginzburg-Ziv theorem. This work begins the off-diagonal case
of the results of Bialostocki, Erdos, and Lefmann.
