In this paper we present sorting algorithms on the recently introduced N2 processor OTIS-Mesh, a network with diameter 4 p N , 3 consisting of N connected meshes of size p N p N. We show that k-k sorting can be done in 8 p N + ON 1 3 steps for k = 1;2;3;4 and in 2k p N + OkN 1 3 steps for k 4 with constant buffersize for all k. We show how our algorithms can be modified to achieve 4 p N+ON 1 3 steps for k = 1;2;3;4and k p N+OkN 1 3 steps for k 4 in the average case. Finally we show a lower bound of maxf4 p N; 1p2 k p Ngsteps for k-k sorting.