Using the strain gauge technique, the magnetostriction constants ¿ and ¿ have been measured on single crystals of CoxFe3-xO4 with compositions 0.0005=x=0.1 in the temperature range between 100 and 300 K and using magnetic fields up to 23 kOe. The presence of Co2+-ions gives rise to a very large negative value of ¿ and a fairly large positive value of ¿. A linear relationship is found between the magnetostriction constants and the cobalt concentration. Some conclusions about the anisotropic beheviour of the samples can be made, based on the magnetostriction measurements. The change of the direction of easy magnetization from  to  in the temperature range just above the Verwey transition, is illustrated and discussed. It turned out to be possible to determine an effective anisotropy constant K'1 through a curve fitting procedure. It is found that 1n K'1 varies linearly with T.