  The stability of the Lagrangian point $L_4$ is investigated in the elliptic
restricted three-body problem by using Floquet's theory. Stable and unstable
domains are determined in the parameter plane of the mass parameter and the
eccentricity by computing the characteristic exponents. Frequencies of motion
around $L_4$ have been determined both in the stable and unstable domains and
fitting functions for the frequencies are derived depending on the mass
parameter and the eccentricity. Resonances between the frequencies are studied
in the whole parameter plane. It is shown that the 1:1 resonances are not
restricted only to single curves but extend to the whole unstable domain. In
the unstable domains longer escape times of the test particle from the
neighbourhood of $L_4$ are related to certain resonances, but changing the
parameters the same resonances may lead to faster escape.
