High-spin states in the odd-proton thulium isotopes 173Tm and 175Tm have been studied using deep-inelastic reactions and γ-ray spectroscopy. In 173Tm, the low-lying structure has been confirmed and numerous new states have been identified, including a three-quasiparticle Kπ= 19/2− isomer with a lifetime of τ=360(100) ns at 1906 keV and a five-quasiparticle Kπ=35/2− isomer with a lifetime of τ= 175(40) ns at 4048 keV. The Kπ=35/2− state is interpreted as a t-band configuration that shows anomalously fast decays. In 175Tm, the low-lying structure has been reevaluated, a candidate state for the 9/2−[514] orbital has been identified at 1175 keV, and the 7/2−[523] bandhead has been measured to have a lifetime of τ= 460(50) ns. Newly identified high-K structures in 175Tm include a Kπ=15/2− isomer with a lifetime of τ= 64(3) ns at 947 keV and a Kπ= 23/2+ isomer with a lifetime of τ= 30(20) μs at 1518 keV. The Kπ=15/2− isomer shows relatively enhanced decays to the 7/2−[523] band that can be explained by chance mixing with the 15/2− member of the 7/2− band. Multiquasiparticle calculations have been performed for 173Tm and 175Tm, the results of which compare well with the experimentally observed high-spin states.