Magnetic cycles analogous to the solar cycle have been detected in tens of solar-like stars by analyzing long-term time series of different magnetic activity indexes. The relationship between the cycle properties and global stellar parameters is not fully understood yet. One reason for this is the lack of long-term time series for stars covering a wide range of stellar parameters. We searched for activity cycles in a sample of 90 young solar-like stars with ages between 4 and 95 Myr with the aim to investigate the properties of activity cycles in this age range. We measured the length P_cyc_ of a given cycle by analyzing the long-term time series of three different activity indexes: the period of rotational modulation, the amplitude of the rotational modulation and the median magnitude in the V band. For each star, we also computed the global magnetic activity index <IQR> that is proportional to the amplitude of the rotational modulation and can be regarded as a proxy of the mean level of the surface magnetic activity. We detected activity cycles in 67 stars. Secondary cycles were also detected in 32 stars of the sample. The lack of correlation between P_cyc_ and P_rot_ and the position of our targets in the P_cyc_/P_rot_-Ro^-1^ diagram suggest that these stars belong to the so-called transitional branch and that the dynamo acting in these stars is different from the solar dynamo and from that acting in the older Mt. Wilson stars. This statement is also supported by the analysis of the butterfly diagrams whose patterns are very different from those seen in the solar case. We computed the Spearman correlation coefficient r_S_ between P_cyc_, <IQR> and various stellar parameters. We found that P_cyc_ in our sample is uncorrelated with all the investigated parameters. The <IQR> index is positively correlated with the convective turnover timescale, the magnetic diffusivity timescale {tau}_diff_, and the dynamo number D_N_, whereas it is anti-correlated with the effective temperature Teff, the photometric shear {Delta}{Omega}_phot_ and the radius R_C_ at which the convective zone is located. We investigated how P_cyc_ and <IQR> evolve with the stellar age. We found that P_cyc_ is about constant and that <IQR> decreases with the stellar age in the range 4-95Myr. Finally we investigated the magnetic activity of the star AB Dor A by merging All Sky Automatic Survey (ASAS) time series with previous long-term photometric data. We estimated the length of the AB Dor A primary cycle as P_cyc_=16.78+/-2yr and we also found shorter secondary cycles with lengths of 400d, 190d, and 90d, respectively.