The cellulose Lyocell fibre spinning process can be divided into two processes, a dry spinning process in the air gap, and a wet spinning process in the coagulation bath. In order to simulate the process in the air gap, the heat capacity Cp, the density ρ, and the elongational viscosity ɳ were measured by experiments carried out as a function of temperature and concentration of cellulose. The calculated diameters and temperature profiles along the spinning path were compared with the experimental results. The concentration of N-methyl-morpholine-N-oxide (NMMO) in the fibre (in the coagulation bath) was also measured during the experiments, and the diffusion coefficient was then calculated. Using the data obtained, the time during which the NMMO content in the fibre reaches the equilibrium state in the coagulation bath can be predicted.