A nonequilibrium thermodynamic model based on the interfacial transport phenomena (ITP) formalism was used to study deformation-relaxation behavior of water-in-water emulsions. The ITP formalism allows us to describe all water-in-water emulsions with one single theory. Phase-separated biopolymer solutions, hydrogel beads, liposomes, polymersomes, colloidosomes, and aqueous polymer microcapsules are all limiting cases of this general theory with respect to theological behavior of the bulk phases and interfaces. Here we have studied two limiting cases of the general theory, with negligible surface rheology: phase-separated biopolymer solutions and hydrogel beads. We have determined the longest relaxation time for a small perturbation of the interfaces in these systems. Parameter maps were calculated which can be used to determine when surface tension, bending rigidity, permeability, and bulk viscoelasticity dominate the response of a droplet or gel bead. In phase-separated biopolymer solutions and dispersions of hydrogel beads six different scaling regimes can be identified for the relaxation time of a deformation. Hydrogel beads may also have a damped oscillatory response to a deformation. The results presented here provide new insight into the complex dynamics of water-in-water emulsions and also suggest new experiments that can be used to characterize the interfacial properties of these systems.