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tokens: prior. Since we benefitted from transit observations that span more than three years, we did not use a prior on the period and time of inferior conjunction of the transiting planet. 3.4. Results We present in Table 3 the median and 1 limits of the marginalised posterior distributions after running five chains of 100 000 accepted steps (considering a 20% burn-in phase). The acceptance rate is 25% (40% for the burn-in phase). The convergence of the chains is validated by the test of Gelman Rubin (1992) (PSFR better than 1.01), and the autocorrelations are shorter than 2000 steps. Including the second planet in the model undoubtedly improves the fit. The rms of the CORALIE data after the two-planet fit is ten times smaller than after a one-planet fit. The best fit solution is plotted in Fig. 8 for the transit light curves and in Fig. 9 for the radial velocities. Again, the values provided in Table 3 are not the ones used in Figs. 9 and 8 . We checked that they represent a self-consistent set of parameters by comparing the BIC using both sets of values (best fit and median of the posterior distribution) and get compatible results. Table 3 Median and 1 limits of the posterior marginalised PDFs obtained for the WASP-41 system derived from our global MCMC analysis. Notes. (*) Assuming zero albedo and efficient redistribution of energy. Fig. 8 WASP-41b transit data (blue: FTS ; green: TRAPPIST ; red: Danish ) and best fit model (black line). The TRAPPIST light curve was obtained by binning the data from five transit observations, and the Danish one from one full and one partial transit observations. Each point corresponds to a 7.2 min bin. Fig. 9 WASP-41 radial velocity data (blue: CORALIE, green: HARPS; red: HARPS RM sequence) and best fit model (black line). Top : phase-folded on the period of the inner planet (outer planet subtracted). Middle : zoom on the Rossiter-McLaughlin effect. Bottom : phase-folded on the period of the outer planet (inner planet subtracted). The best-fitting model suggests a misaligned planet with a projected orbital obliquity of . However, the uncertainties are large (see Fig. 10 ), and the data do not allow an aligned orbit to be excluded (). The rotation velocity expected from the photometric rotation period of the star (2.44 km s) is compatible within the error bars with the spectroscopic (2.64 0.25 km s), suggesting that the star is equator-on. That reinforces the possibility of an aligned planet. 4. Discussion We have shown that finding long-period planets with instruments such as CORALIE is still possible around active stars. Recognising the periodic structure of activity-related signals is essential to avoiding false detections. While spots or plages induce signals at the rotation period of the star, the evolution of their coverage of the stellar surface is correlated with the magnetic cycle of the star. Such cycles have periods of several years and must be distinguished from long-period companions. Lovis et al.