A theoretical analysis shows factors which affect the onset of nonlinear response of the anode current of a photomultiplier to the light intensity incident on the photocathode, when the dynode voltages are provided by a linear resistor chain. The percent deviation from linearity of the anode current is shown to be independent of the number of dynodes and the gain per stage. The conditions do depend on the form of the gain per stage which is assumed to depend on parametersg=p+q. The parametergis shown to have approximately the same value for a number of photomultipliers, so that any significant differences in the initial deviation from linearity would be attributed to the ratiop/q. This ratio has not been measured, but a method of doing so is described. Some measurements of the deviation from linearity are discussed in terms of the analysis, and the indications from that limited sampling are that one can expect deviations to be less than 3% for all photomultipliers when the anode current is less than 0.1 the current in the final resistor of a linear bleeder chain.