Co2+:II-VI chalcogenide (e.g. ZnSe, ZnS) crystals exhibit broad emission in the 3-4µm spectral range with absorption peaks at ~0.75µm, ~1.5µm, and ~2.9µm which can be used for excitation. Laser oscillation of Fe2+ with wavelength ~4µm has been demonstrated at 14K in Co:Fe:ZnSe/ZnS under energy transfer from Co2+ ions. However, recent efforts in obtaining laser oscillation in Co2+:ZnSe/ZnS crystals have been unsuccessful. This can potentially be explained by excited state absorption at the 4T2(F)→4T1(F) transition. In addition, the laser oscillation in Co:Fe:ZnSe/ZnS co-doped crystals was only observed at temperatures under 21K. We report measurements of Co:ZnSe/ZnS absorption and emission at room temperature and 14K as well as estimates of excited state absorption from these measurements. Also, the results of experiments showed increase of absorption at 2.94µm under alexandrite laser excitation in Co:ZnS, which could result from excited state absorption. The lifetime of induced absorption was ~100µs, which is close to the ~200µs lifetime of the 4T2 level. The model of excited state absorption at low temperature predicts strong absorption over the emission spectrum of Co2+ in ZnSe, which can explain the negative lasing results. The loss of laser oscillation in co-doped crystals with increased temperature can be explained by the broadening of excited state absorption of Co2+. The spectroscopic measurements of the excited state absorption spectrum of Co:ZnSe/ZnS will be presented at the conference.