  A majority part of magnetic chemically peculiar (mCP) stars of the upper main
sequence exhibits strictly periodic light, magnetic, radio, and spectral
variations that can be fully explained by the model of a rigidly rotating
main-sequence star with persistent surface structures and stable global
magnetic field frozen into the body of the star. Nevertheless, there is an
inhomogeneous group consisting of a few mCP stars whose rotation periods vary
on timescales of decades, while the shapes of their phase curves remain nearly
unchanged. Alternations in the rotational period variations, proven in the case
of some of them, offer new insight on this theoretically unpredicted
phenomenon. We present a novel and generally applicable method of period
analysis based on the simultaneous exploitation of all available observational
data containing phase information. This phenomenological method can monitor
gradual changes in the observed instantaneous period very efficiently and
reliably. We present up to date results of the period monitoring of V901~Ori,
CU~Vir, $\sigma$\,Ori\,E, and BS~Cir, known to be mCP stars changing their
observed periods and discuss the physics of this unusual behaviour. To compare
the period behavior of those stars, we treated their data with an orthogonal
polynomial model, which was specifically developed for this purpose. We
confirmed period variations in all stars and showed that they reflect real
changes in the angular velocity of outer layers of the stars, fastened by their
global magnetic fields. However, the nature of the observed rotational
instabilities has remained elusive up to now. The discussed group of mCP stars
is inhomogeneous to such extent that each of the stars may experience a
different cause for its period variations.
