The annihilatorsN, Mof the input and output maps,B,C, respectively of the linear state space modelS(A, B, C) led to theNAMalgorithm for the calculation of system zeros. A recent paper proposed an alternative algorithm and the present paper undertakes a comparison between the two. It is shown that the new approach resembles theNAMalgorithm and indeed, in all but the general case the two approaches are shown to be conceptually identical ; in the general case the new method fails to identify the precise set of zeros and this obviates the need for a comparison. An examination of the computational aspects however demonstrates the advantages of the NAM algorithm in both the calculation of zeros and zero directions.