A version of Schwinger's action principle is presented. There are two classes of variations, denoted S and G . The class S consists of generators of allowable variations of the dynamical variables q and the class G consists of allowable additions to the Lagrangian. The Cartesian product S × G must belong to the kernel space of an antisymmetric bilinear map R, so that if S is chosen to be large then G must be small. Different choices of S and G lead to different commutation relations for the q's. If S and G are both required to contain generators N ij of linear transformations of the q's, then the vanishing of R( N ij , N kl ) implies that the q's obey paracommutation relations. The stationary property of the action is guaranteed by an equation of motion of the usual type provided that the Hamiltonian belongs to the class G . When the q's obey paracommutation relations, R( N ij , Γ) vanishes for all Γ. So if S is restricted to linear variations then G (and thus the Hamiltonian) is unrestricted. Conversely, when G is unrestricted, S is restricted to linear variations.