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We have searched for continuous gravitational wave (CGW) signals produced byindividually resolvable, circular supermassive black hole binaries (SMBHBs) inthe latest EPTA dataset, which consists of ultra-precise timing data on 41millisecond pulsars. We develop frequentist and Bayesian detection algorithmsto search both for monochromatic and frequency-evolving systems. None of theadopted algorithms show evidence for the presence of such a CGW signal,indicating that the data are best described by pulsar and radiometer noiseonly. Depending on the adopted detection algorithm, the 95\% upper limit on thesky-averaged strain amplitude lies in the range $6\times10^{-15}<A<1.5\times10^{-14}$ at $5{\rm nHz}<f<7{\rm nHz}$. This limit variesby a factor of five, depending on the assumed source position, and the mostconstraining limit is achieved towards the positions of the most sensitivepulsars in the timing array. The most robust upper limit -- obtained via a fullBayesian analysis searching simultaneously over the signal and pulsar noise onthe subset of ours six best pulsars -- is $A\approx10^{-14}$. These limits, themost stringent to date at $f<10{\rm nHz}$, exclude the presence ofsub-centiparsec binaries with chirp mass $\cal{M}_c>10^9$M$_\odot$ out to adistance of about 25Mpc, and with $\cal{M}_c>10^{10}$M$_\odot$ out to adistance of about 1Gpc ($z\approx0.2$). We show that state-of-the-art SMBHBpopulation models predict $<1\%$ probability of detecting a CGW with thecurrent EPTA dataset, consistent with the reported non-detection. We stress,however, that PTA limits on individual CGW have improved by almost an order ofmagnitude in the last five years. The continuing advances in pulsar timing dataacquisition and analysis techniques will allow for strong astrophysicalconstraints on the population of nearby SMBHBs in the coming years.

European Pulsar Timing Array Limits on Continuous Gravitational Waves from Individual Supermassive Black Hole Binaries