Context. Magnetic cycles analogous to the solar one 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 sparseness of the data. Aims. In the present paper 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. Methods. 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 computed also the global magnetic activity index 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. Results. 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 one 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 , and different stellar parameters. We found that P cyc in our sample is uncorrelated with all the investigated parameters. The index is positively correlated with the convective turn-over time-scale, the magnetic diffusivity time-scale τ diff , and the dynamo number D N , whereas it is anti-correlated with the effective temperature T eff , the photometric shear ∆Ω phot and the radius R C at which the convective zone is located. We investigated how P cyc and evolve with the stellar age. We found that P cyc is about constant and that decreases with the stellare age in the range 4-95 Myr. Finally we investigated the magnetic activity of the star AB Dor A by merging 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 found also shorter secondary cycles with lengths of 400 d, 190 d and 90 d respectively.