The Lagrangian describing the dynamic system contains high-order time derivatives of the generalized coordinates, which characterizes a high-order derivative system. This framework generalizes classical Lagrangian mechanics. Noether theorem reveals the intrinsic relationship between symmetry and conserved quantities, and provides a unified method for constructing conservation laws of systems. The Herglotz principle extends the Hamilton principle to nonconservative systems by introducing an action defined by a differential equation, providing a new method for dealing with dissipative forces. This paper studies the Herglotz-type Noether theorem and its inverse theorem for nonconservative high-order derivative systems, as well as for nonconservative high-order derivative systems subject to first-order nonholonomic constraints. First, for the high-order derivative system, the equations of motion are derived from the Herglotz-type variational principle. Based on the invariance of the Hamilton-Herglotz action under infinitesimal group transformations, the definition of Noether symmetry is provided, and the corresponding Noether identity is derived. The Noether theorem for the system is then established, along with its inverse theorem. Next, for the high-order derivative system with first-order constraints, the Herglotz–Routh equation of motion is derived using the Lagrange multiplier method. Combined with the Appell–Chetaev condition, the Noether theorem and its inverse for such systems are presented. Finally, for specific examples, the conservation laws without nonholonomic constraints and with nonholonomic constraints are studied, respectively. Through specific example analysis, the correctness of the method is verified.