Excited-state absorption (ESA) is a key process for upconversion pumping schemes of thulium (Tm3+) doped laser materials. We have systematically studied two ESA transitions in the near-infrared spectral range, namely 3F4 → 3F2,3 (at ∼1 µm) and 3F4 → 3H4 (at ∼1.5 µm), in various Tm3+-doped fluoride (ZBLAN glass, cubic KY3F10 and CaF2, tetragonal LiYF4 and LiLuF4, monoclinic BaY2F8 crystals) and oxide (cubic Y3Al5O12, orthorhombic YAlO3 crystals) laser materials, using a pump-probe method with a polarized light. An approach to calculate the constants of energy-transfer upconversion (ETU) is also presented.