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Position-sensitive photomultiplier tubes with fine-mesh-structured dynodes and discrete-anode-array configurations are discussed. One photomultiplier tube, constructed with 88 multianodes, has a spatial resolution of less than 2.6 mm FWHM in a magnetic field with a density of 500-2000 G; it is being used as a photodetector for high-energy physics applications in high-magnetic-field environments. Another type of multianode photomultiplier tube that has been developed functions as a high-spatial-resolution detector for positron-emission tomography (PET) and scintillation-system hodoscopes. By applying additional electrofocusing electrodes to this tube, an intrinsic spatial resolution of 1.4 mm FWHM without the magnetic field can be obtained.