We present the results of our spectroscopic monitoring observations of the late O-type runaway stars AE Aur and iota Ori, carried out between September 2016 and May 2018 using the Echelle spectrograph FLECHAS at the University Observatory Jena. For both stars, we obtained current radial velocity (RV) measurements with better precision than before. These results can be used for further advanced calculations of their space motion, needed to determine, for example, their place of origin in our Galaxy. In this paper, we describe the observations and the data reduction, as well as the analysis of all spectral data. We find a stable RV for AE Aur and confirm iota Ori as a double-lined spectroscopic binary and derive its current Keplerian orbital elements.