A J/sup ..pi../ = (25/2)/sup +/ isomer in /sup 205/Tl has been observed using techniques of in-beam ..gamma..-ray spectroscopy and the /sup 204/Hg(t,2n)/sup 205/Tl reaction. The decay scheme firmly establishes the yrast levels: (J/sup ..pi../,E/sub x/ (keV)) (11/2)/sup -/, 1484.02; (15/2)/sup -/, 2054.57; (17/2)/sup -/, 2394.18; (19/2)/sup -/, 2551.56; and (25/2)/sup +/, 3290.7. A candidate for a 12/sup -/ state in /sup 204/Tl with the configuration (..pi..h/sub 11/2/ /sup -1/, ..nu..i/sub 13/2/ /sup -1/) is identified.