Two limitation methods, A and B , are said to be consistent for a class b of sequences, iff, every sequence belonging to b is limitable both by A and B and that the A -limit equals the B -limit. Any two regular limitation methods are consistent for the class- c of convergent sequences. However, this is not true in general and in fact, corresponding to every bounded non-convergent sequence it is possible to determine two T -matrices such that they limit the sequence to two different values. In this paper, we establish the necessary and sufficient conditions for the consistency of two limitation methods, for ( N , p n ) summable sequences.