The motion of cells, within the extracellular liquid, is induced by a chemical attractant. Here the cell population, the attractant, and the liquid are modelled within continuum mechanics as a mixture of three constituents. The active character of the cells is expressed by a body force proportional to the gradient of the attractant density. The balance equations of mass and linear momentum are developed and the density of cell population is shown to satisfy a hyperbolic equation. The characteristic features of previous models of chemotaxis are also investigated and evidence is given to the assumptions that lead to parabolic equations.