  Generalized Super-\v{C}erenkov Radiations (S\v{C}R), as well as their
S\v{C}R-signatures are investigated. Two general S\v{C}R-coherence conditions
are found as two natural extremes of the same spontaneous particles decays in
(dielectric, nuclear or hadronic) media. The main results on the experimental
test of the super-coherence conditions, obtained by using the experimental data
from BNL, are presented. The interpretation of the observed anomalous
\v{C}erenkov rings as experimental evidence for the HE-component of the S\v{C}R
is discussed.
