  We investigate the photometric modulation induced by magnetic activity cycles
and study the relationship between rotation period and activity cycle(s) in
late-type (FGKM) stars. We analyse light-curves spanning up to 9 years of 125
nearby stars provided by the ASAS survey. The sample is mainly conformed by
low-activity main sequence late A to mid M-type stars. A search is performed
for short (days) and long-term (years) periodic variations in the photometry.
We modelled with combinations of sinusoids the light-curves to measure the
properties of these periodic signals. To provide a better statistical
interpretation of our results we complement them with the results from previous
similar works. We have been able to measure long-term photometric cycles of 47
stars. Rotational modulation was also detected and rotational periods measured
in 36 stars. For 28 stars we have simultaneous measurements of both, activity
cycles and rotational periods, being 17 of them M-type stars. From sinusoidal
fits we measured both photometric amplitudes and periods. The measured cycle
periods range from 2 up to 14 yr with photometric amplitudes in the range of
5-20 mmag. We have found that the distribution of cycle lengths for the
different spectral types is similar. On the other hand the distribution of
rotation periods is completely different, trending to longer periods for later
type stars. The amplitudes induced by magnetic cycles and rotation show a clear
correlation. A trend of photometric amplitudes with rotation period is also
outlined in the data. For a given activity index the amplitudes of the
photometric variability induced by activity cycles of main sequence GK stars
are lower than those of early and mid-M dwarfs. Using spectroscopic data we
also provide an update in the empirical relationship between the level of
chromospheric activity as given by log(Rhk) and the rotation periods.
