We report on synthesis and characterization of doubly temperature sensitive core-shell microgels. These core-shell microgels are composed of a core of chemically cross-linked poly(N-isopropylacrylamide) (PNIPAM) and a shell of cross-linked poly(N-isopropylmethacrylamide) (PNIPMAM). PNIPAM exhibits in water a lower critical solution temperature (LCST) of ca. 34 degreesC, and the LCST of PNIPMAM is ca. 45 degreesC. Solution properties were investigated by means of dynamic light scattering (DLS), optical transmission, differential scanning calorimetry (DSC), and small-angle neutron scattering (SANS). Core-shell microgels of this composition display a temperature-dependent two-step shrinking behavior. The influences of the content of the cross-linking agent N'-methylenbis(acrylamide) (BIS) and of the thickness of the PNIPMAM shell on the thermosensitive response of the PNIPAM/PNIPMAM core-shell microgels were investigated. Core-shell microgels with a thick shell do not show a size transition at the PNIPAM LCST anymore. The volume transition is adjustable by varying the cross-link density of the shell. The swelling behavior of the core-shell microgels is compared to that of pure PNIPAM and PNIPMAM. Additionally, an inverse system consisting of a PNIPMAM core and a PNIPAM shell was prepared and investigated by DLS. Here the collapsed shell at intermediate temperatures strongly restricts the core swelling so that the overall size of the core-shell microgel is smaller as compared to the pure core.