Critical phenomena observed by electron paramagnetic resonance (EPR) near the phase transitions of SrTiO3 and LaAlO3 are reviewed. A short description of the second-order antiferrodistortive transitions in these compounds is first given. Then high accuracy EPR Fe3+ measurements of the temperature dependence of the (rotational) order parameter φ are described. These show the existence of a critical region near Tc in both compounds which scale and yield the static critical exponents β and γ. A survey of the EPR linewidth broadening of the Fe3+i-V0 centre in SrTiO3 due to the critical slowing down of local order parameter fluctuations follows. The frequency width ∆ω(T) of the local spectral density narrows strongly on approaching Tc. Close to Tca quasi-static regime is created. This allows a determination of the probability distribution P(φl) from the EPR lineshapes. P(φl) deviates from a Gaussian closely above and below Tc. © 1974, Taylor & Francis Group, LLC. All rights reserved.