  In this paper, non-Hamiltonian systems with holonomic constraints are treated
by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can
be described by generalized antisymmetric brackets or by general Liouville
operators which cannot be derived from brackets. Both situations are treated.
In the first case, a Nos\'e-Dirac bracket is introduced as an example. In the
second one, Dirac's recipe for projecting out constrained variables from time
translation operators is generalized and then applied to non-Hamiltonian linear
response. Dirac's formalism avoids spurious terms in the response function of
constrained systems. However, corrections coming from phase space measure must
be considered for general perturbations.
