  The dynamics of small bodies around the Earth has gained a renewed interest,
since the awareness of the problems that space debris can cause in the nearby
future. A relevant role in space debris is played by lunisolar secular
resonances, which might contribute to an increase of the orbital elements,
typically of the eccentricity. We concentrate our attention on the lunisolar
secular resonance described by the relation $2\dot{\omega}+\dot{\Omega}=0$,
where $\omega$ and $\Omega$ denote the argument of perigee and the longitude of
the ascending node of the space debris. We introduce three different models
with increasing complexity. We show that the growth in eccentricity, as
observed in space debris located in the MEO region at the inclination about
equal to $56^\circ$, can be explained as a natural effect of the secular
resonance $2\dot{\omega}+\dot{\Omega}=0$, while the chaotic variations of the
orbital parameters are the result of interaction and overlapping of nearby
resonances.
