We report on reflection high energy electron diffraction (RHEED) studies of molecular beam epitaxy (MBE) growth of CdTe and CdMnTe on (100) oriented CdTe substrates. RHEED oscillations were measured for both the growth and desorption of CdTe and CdMnTe as a function of flux and temperature. For the first time, the influence of laser and electron irradiation on the growth rate, as well as desorption, of CdTe is studied in detail using RHEED oscillations. We found a very small effect on the growth rate as well as on the CdTe desorption rate. The growth rate of CdTe was determined for different temperatures and CdTe flux ratios. The obtained experimental results are compared with a kinetic growth model to get information on the underlying growth processes, taking into account the influence of a precursor by including surface diffusion. From the comparison between model and experimental results the sticking coefficients of Cd and Te are determined. The growth rate of CdMnTe increases with Mn flux. This dependence can be used to calibrate the Mn content during growth by comparing the growth rate of CdTe with the growth rate of CdMnTe. The change in growth rate has been correlated with Mn content via photoluminescence measurements. In addition, the sticking coefficient of Mn is derived by comparing experimental results with a kinetic growth model. For high manganese content a transition to three-dimensional growth occurs.