We searched for X-ray counterparts of optical novae detected in M 31 and M 33. We combined an optical nova catalogue from the WeCAPP survey with optical novae reported in the literature and correlated them with the most recent X-ray catalogues from ROSAT, XMM-Newton, and Chandra, and in addition searched for nova correlations in archival data. We report 21 X-ray counterparts for novae in M 31 mostly identified as supersoft sources (SSS) by their hardness ratios and two in M 33. Our sample more than triples the number of known optical novae with a supersoft X-ray phase. Most of the counterparts are covered in several observations allowing us to constrain their X-ray light curves. Selected brighter sources were classified by their XMM-Newton EPIC spectra. We use the well-determined start time of the SSS state in two novae to estimate the hydrogen mass ejected in the outburst to ~10-5~M&sun; and ~10-6~M&sun;, respectively. The supersoft X-ray phase of at least 15% of the novae starts within a year. At least one of the novae shows a SSS state lasting 6.1 years after the optical outburst. Six of the SSSs turned on between 3 and 9 years after the optical discovery of the outburst and may be interpreted as recurrent novae. If confirmed, the detection of a delayed SSS phase turn-on may be used as a new method to classify novae as recurrent. At the moment, the new method yields a ratio of recurrent novae to classical novae of 0.3, which is in agreement (within the errors) with previous works.