Abstract.Let T denote the algebra of all bounded infinite matrices on c , the space of convergent sequences, A the subalgebra of T consisting of lower triangular matrices. It is well known that, if H is any HausdorfT matrix with distinct diagonal entries, then the commutant of H in A contains only HausdorfT matrices. In previous work the author has shown that a necessary condition for the commutant of a HausdorfT matrix H to be the same in T and A is that H have distinct diagonal entries, but that the condition is not sufficient. In this paper it is shown that certain HausdorfT matrices, with distinct diagonal entries, have the same commutants in F and A .Let Jf be the set of all doubly infinite matrices, 38 c JÍ the subalgebra of infinite matrices with the finite norm, where ||5|| := sup" \J,k \ank\. Let ST C JH be the subalgebra consisting of lower triangular matrices. HausdorfT [7] showed that, if 77 is any HausdorfT matrix with distinct diagonal entries, then the commutant of H in ¿7" consists of HausdorfT matrices.Let T be the subalgebra of Jf consisting of all bounded infinite matrices on c, the space of convergent sequences, A the subalgebra of T composed of triangular matrices.In papers [6] and [7] the author showed that there exist HausdorfT matrices with distinct diagonal entries that have non-Hausdorff matrices in the commutant, and that a necessary condition for the commutant of a HausdorfT matrix in T and A to be the same is that H have distinct diagonal entries.The author [6] and Jakimovski [4] have independently shown that the cornmutant of (C, I), the Cesàro matrix of order 1, in T, is %?, the set of conservative HausdorfT matrices. (A matrix is conservative if it is convergencepreserving over c.) However, the proof only uses the fact that A, (C, 1 ) e 38 . It is well known that, if a HausdorfT matrix has finite norm, then automatically it has all zero column limits, except possibly for the first column, and the first column converges. Since every HausdorfT matrix has row sums equal to po, the Silverman-Toeplitz conditions Tor a matrix to be conservative are satisfied, and the matrix is conservative. Thus the commutants oT (C, I) in A and in 38