This paper utilizes the concept of almost homogeneity to obtain a generalization of the elasticity of factor substitution. From this, an expression for the bias to technical change is derived that explicitly includes the individual degrees of input homogeneity. It is shown that the relative values of these homogeneity parameters can affect the magnitude and direction of the factor-saving bias to technical change. These parameters also influence the size of the residual or unexplained component of aggregate output growth.