By virtue of a modulation technique, positive charge carriers in single-layer-light emitting diodes (LEDs) made from molecularly doped polymers can be identified with molecular radical cations. Using the characteristic cation absorption spectra enables measurement of the number of positive charge carriers present in a LED under operation conditions. A straightforward calculation yields the corresponding hole mobilities, The effect of the concentration of dopant molecules and of the matrix polarity on the mobility is discussed with reference to results from time-of-flight (TOF) studies on molecularly doped polymers in conjunction with Monte-Carlo simulations and their interpretation in terms of the disorder model in the limit of high electric field. The disagreement between the optically determined mobilities and the corresponding values obtained on the premise that the delayed onset of electroluminescence reflects the transit time of majority carriers indicate that this assignment is incorrect.