We have investigated the low-temperature behaviour of the dielectric c
onstant of the mixed crystal (KBr)1-x(KCN)x for x = 0.01 and x = 0.001
. The experiments were performed at microwave frequencies between 150
and 1227 MHz in the temperature range from 0.015 K to 10 K. Our experi
ments prove the existence of tunnelling states with a very small and n
arrowly distributed energy splitting near E/k(B) = 10 mK for x = 0.001
. E increases with CN- concentration and reaches E/k(B) = 40 mK for x
= 0.01. These states occur in addition to those at 1 K, well known fro
m thermal experiments.