Immediate and near-future plans for transmission positron microscopes being built at KEK, Tsukuba, Japan, are described. The characteristic feature of this project is remolding a commercial electron microscope to a positron microscope. A point source of electrons kept at a negative high voltage is changed to a point source of positrons kept at a high positive voltage. Positional resolution of transmission microscopes should be theoretically the same as electron microscopes. Positron microscopes utilizing trapping of positrons have always positional ambiguity due to the diffusion of positrons. (c) 2005 Elsevier B.V. All rights reserved.