We demonstrate a confocal optical microscope that combines cw two-photon-excited fluorescence microscopy with confocal Raman microscopy. With this microscope fast image acquisition with fluorescence imaging can be used to select areas of interest for subsequent chemical analysis with spontaneous Raman imaging. The distribution of the UV-absorbing fluorophore Hoechst 33342 in the apoptotic HeLa cells is measured in the combined cw two-photon-excited fluorescence and Raman microscopy modes. The 647-nm line of a Kr-ion laser is used to excite both the Raman scattering and the two-photon-excited fluorescence emission. The lateral and axial resolutions in the two imaging modes are compared by use of the Gaussian beam approximation and backprojection of the focal volume through the confocal pinhole.