  In this paper we present radial velocity curves of AGB variables that exhibit
various kinds of anomalies: Semiregular variables (SRVs) with typical mira
periods, SRVs exceeding the mira 2.5 mag amplitude limit, miras with secondary
maxima in their light curves, and a SRV with a long secondary period. The stars
with reliable Hipparcos parallaxes from this and from previous studies are
plotted in a logP-$M_{K}$-diagram. Our objects nicely follow the
logP-$M_{K}$-relations determined for the LMC. This allows the pulsation mode
to be identified. While all miras fall on the fundamental mode sequence, the
SRVs fall on both the first overtone and fundamental mode sequences. The SRVs
on the fundamental mode sequence occur at both high and low luminosities, some
of them being more luminous than larger amplitude miras. This demonstrates
observationally that some parameter other than luminosity affects the stability
of long period variables, probably mass. First overtone pulsators all show
velocity amplitudes around 4 km/s. For the fundamental mode pulsators, the
velocity amplitude shows a correlation with light amplitude. The two miras R
Cen and R Nor, known for their double-peaked light curves, have velocity curves
that are quite different. The R Nor velocity curve shows no evidence of the
double peaks, meaning that the true pulsation period is the time between
alternate minima or maxima. There is slight evidence for a double bump in the R
Cen velocity curve. It is suggested that these stars are relatively massive
(3-5 Msun).
