We study structure-preserving algorithms to phase space volume for linear dynamical systems y = Ly for which arbitrarily high order explicit symmetric structure-preserving schemes,i.e. the numerical solutions generated by the schemes satisfy det(()yo/()y1) = ehtrL,where trL is the trace of matrix L, can be constructed. For nonlinear dynamical systems y = f(y) Feng-Shang first-order volume-preserving scheme can be also constructed starting from modified θ - methods and is shown that the scheme is structure-preserving to phase space volume.