Sensitive microgels are submicrometer sized, cross-linked polymer particles with a unique swelling behavior changing in response to surrounding conditions like temperature, pH and ionic strength. In this study we influence the swelling capability of thermosensitive microgels microgel by the composition of the solvent (cononsolvency). In particular, we investigate the effects on the structure and dynamics of poly(N-isopropylacrylamide) (PNIPAM) and poly(N,N-diethylacrylamide) (PDEAAM) microgels with different degree of swelling in MeOD/D2O solvent mixture at 10 degrees C using a combination of small angle neutron scattering (SANS) and neutron spin echo (NSE) spectroscopy at nanoseconds scales in the range of several nanometers. The structural characterization including size and density profiles was determined by fitting SANS data. The dynamical behavior of partially collapsed and swollen microgels is comprehensively described within the theory of semidilute polymers in solutions where hydrodynamic interactions are dominant. The partially collapsed PNIPAM microgel particles are not solid diffusing objects but they have relevant contributions from internal motions. Thus, Zimm segmental dynamics can be detected with elevated apparent viscosity. The swollen PDEAAM microgel particles have a faster internal dynamics compared to the partially collapsed PNIPAM. It can also be explained by Zimm-like relaxations with relatively high apparent viscosity and an additional diffusive contribution coming from the cross-linkers.