We have implemented simultaneous picosecond pulsed two- and three-photon excitation of near-UV and visible absorbing fluorophores in a scanning near-field optical microscope (SNOM). The 1064-nm emission from a pulsed Nd:YVO4 laser was used to excite the visible mitochondrial specific dye MitoTracker Orange CM-H2TMRos or a Cy3-labeled antibody by two-photon excitation, and the UV absorbing DNA dyes DAPI and the bisbenzimidazole BBI-342 by three-photon excitation, in a shared aperture SNOM using uncoated fiber tips. Both organelles in human breast adenocarcinoma cells (MCF 7) and specific protein bands on polytene chromosomes of Drosophila melanogaster doubly labeled with a UV and visible dye were readily imaged without photodamage to the specimens. The fluorescence intensities showed the expected nonlinear dependence on the excitation power over the range of 5-40 mW. An analysis of the dependence of fluorescence intensity on the tip-sample displacement normal to the sample surface revealed a higher-order function for the two-photon excitation compared to the one-photon mode. In addition, the sample photobleaching patterns corresponding to one- and two-photon modes revealed a greater lateral confinement of the excitation in the two-photon case. Thus, as in optical microscopy, two-photon excitation in SNOM is confined to a smaller volume.