The recent second‐order theory of Chaffey and Brenner for the deformation of a drop suspended in an immiscible liquid undergoing slow steady shear flow has a narrow range of validity. The deformation parameterDI(proportional to the product of the velocity gradient, the drop radius, the suspending liquid’s viscosity and the reciprocal of the interfacial tension) must be less than 0.24 if the predicted deformation of drops of low viscosity in Couette flow is to be realistic; for highly viscous dropsDImust not exceed 0.1. For all drops in hyperbolic flow and hyperbolic‐radial flowDImust be less than 0.22 and 0.24, respectively. The second‐order approximation,DII,to the observable deformation ratioD(the difference between the drop’s length and width, divided by their sum) exceedsDIfor viscous drops in Couette flow but is slightly smaller thanDIfor drops of low viscosity. Calculated values ofDIIdeviate from experimental data onD. The second‐order theory does predict the lengthening in hyperbolic flow of one drop axis and the shortening of the other two. A new first‐order theory by Cox has a much wider range of validity but does not conflict with the second‐order theory.