  Based on a search for multi-periodic variability among the semi-regular red
variable stars in the database of the All Sky Automated Survey (ASAS), a sample
of 72 typical examples is presented. Their period analysis was performed using
Discrete Fourier Transform. In 41 stars we identified two significant periods
each, simultaneously present, while the remaining 31 cases revealed even three
such periods per star. They occur in a range roughly between 50 and 3000 days.
Inter-relationships between these periods were analyzed using the "double
period diagram" which compares adjacent periods, and the so-called "Petersen
diagram", the period ratio vs. the shorter period. In both diagrams we could
identify six sequences of accumulation of the period values. For five of these
sequences (containing 97% of all data points) we found an almost perfect
coincidence with those of previous studies which were based on very different
samples of semi-regular red variables. Therefore, existence and locations of
these sequences in the diagrams seem to be universal features, which appear in
any data set of semi-regularly variable red giants of the AGB; we conclude that
they are caused by different pulsation modes as the typical and consistent
properties of similar stellar AGB configurations. Stellar pulsations can be
considered as the principal cause of the observed periodic variability of these
stars, and not binary, rotation of a spotted surface or other possible reasons
suggested in the literature.
