Blinking involves high rates of shear within the tear film, requiring a low tear viscosity to avoid damage to epithelial surfaces. Conversely, in the open eye, a higher viscosity is desirable to resist drainage and film break-up. Samples of human tears were collected with moderate stimulation from 5 adult males, 3 with normal and 2 with marginally-dry eyes. The apparent viscosity at 22~ was found using a Couette-type rheometer over the range of shear rate 2-160 sec -1. Marked shear-thinning was apparent in all samples, with little apparent difference between normal and dry-eye tears. Although a power-law equation could be fitted over part of the range, analyses according to either the Casson plastic model as used for rabbit tears (with a low yield-point indicative of some very loose initial gel-like structure) or the Steiger-Ory model (a true pseudoplastic model with no initial yield point) were inconclusive over the range of shear rate studied. The descriptive model of Cross gave zero-shear viscosity values of 4.4, 7.1 and 8.3 mPa.sec for normal tears, and 27.1 and 31.1mPa.sec for dry-eye tears; the corresponding time constants were 0.13, 0.27 and 0.38 sec for normal tears, and 2.7 and 2.9 sec for dry-eye tears. These time-constants can be considered as an approximate relaxation time, indicating the time taken for the tear film to stabilise after a blink.