We derive the general structure for returning to the steady macroscopic nonequilibrium condition, assuming a first-order relaxation equation obtained as zero-cost flow for the Lagrangian governing the dynamical fluctuations. The main ingredient is local detailed balance from which a canonical form of the time-symmetric fluctuation contribution (aka frenesy) can be obtained. That determines the macroscopic evolution. As a consequence, the linear response around stationary nonequilibrium gets connected with the small dynamical fluctuations, leading to fluctuation-response relations. Those results may be viewed as nonequilibrium extension of the well-known structure where the relaxation to equilibrium is characterized by a (dissipative) gradient flow on top of a Hamiltonian motion.