  The thermal and dielectric anomalies of window-type glasses at low
temperatures ($T<$ 1 K) are rather successfully explained by the two-level
systems (2LS) standard tunneling model (STM). However, the magnetic effects
discovered in the multisilicate glasses in recent times, magnetic effects in
the organic glasses and also some older data from mixed
(SiO$_2$)$_{1-x}$(K$_2$O)$_x$ and (SiO$_2$)$_{1-x}$(Na$_2$O)$_x$ glasses
indicate the need for a suitable extension of the 2LS-STM. We show that -- not
only for the magnetic effects, but already for the mixed glasses in the absence
of a field -- the right extension of the 2LS STM is provided by the (anomalous)
multilevel tunnelling systems (A-TS) proposed by one of us for multicomponent
amorphous solids. Though a secondary type of TS, different from the standard
2LS, was invoked long ago already, we clarify their physical origin and
mathematical description and show that their contribution considerably improves
the agreement with the experimental data.
