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In this paper, two types of Schur complement based preconditioners are studied for twofold and block tridiagonal saddle point problems. One is based on the nested (or recursive) Schur complement, the other is based on an additive type Schur complement after permuting the original saddle point systems. We analyze different preconditioners incorporating the exact Schur complements. It is shown that some of them will lead to positive stable preconditioned systems. Our discussion is instructive for devising various exact and inexact preconditioners, as well as iterative solvers for many twofold and block tridiagonal saddle point problems. Numerical experiments for a 3-field formulation of Biot model is provided to justify our theoretical analysis.