The dynamics of polymers on the nm and ns scales inside responsive microgels was probed by means of Neutron Spin Echo (NSE) experiments. Four different microgels were studied: poly(N-isopropylacrylamide) (PNIPAM) and poly(N,N-diethylacrylamide) (PDEAAM) microgels, a P(NIPAM-co-DEAAM) copolymer microgel and a core-shell microgel with a PDEAAM core and a PNIPAM shell. These four different microgel systems were investigated in a D(2)O/CD(3)OD solvent mixture with a molar CD(3)OD fraction of x(MeOD) = 0.2 at 10 °C. The PNIPAM and the P(NIPAM-co-DEAAM) microgels are in the collapsed state under these conditions. They behave as solid diffusing objects with only very small additional contributions from internal motions. The PDEAAM particle is swollen under these conditions and mainly Zimm segmental dynamics can be detected in the intermediate scattering function at high momentum transfer. A cross-over to a collective diffusive motion is found for smaller q-values. The shell of the PDEAAM-core-PNIPAM-shell particle is collapsed, which leads to a static contribution to S(q,t); the core, however, is swollen and Zimm segmental dynamics are observed. However, the contributions of the Zimm segmental dynamics to the scattering function are smaller as compared to the pure PDEAAM particle. Interestingly the values of the apparent solvent viscosities inside the microgels as obtained from the NSE experiments are higher than for the bulk solvent. In addition different values were obtained for the PDEAAM microgel, and the PDEAAM-core of the PDEAAM-core-PNIPAM-shell particle, respectively. We attribute the strongly increased viscosity in the PDEAAM particle to enhanced inhomogeneities, which are induced by the swelling of the particle. The different viscosity inside the PDEAAM-core of the PDEAAM-core-PNIPAM-shell microgel could be due to a confinement effect: the collapsed PNIPAM-shell restricts the swelling of the PDEAAM-core and may modify the hydrodynamic interactions in this restricted environment inside the microgel.