  We describe the phase space structures related to the semi-major axis of
Molniya-like satellites subject to tesseral and lunisolar resonances. In
particular, we dissect the indirect interplay of the critical inclination
resonance on the semi-geosynchronous resonance using a hierarchy of more
realistic dynamical systems, thus discussing the dynamics beyond the integrable
approximation. By introducing \textit{ad hoc} tractable models averaged over
the fast angles, we numerically demarcate the hyperbolic structures organising
the long-term dynamics via the computation of finite-time variational
indicators. Based on the publicly available two-line elements space orbital
data, we identify two satellites, namely M1-69 and M1-87, displaying
fingerprints consistent with the dynamics associated to the hyperbolic set. The
computations of the associated dynamical maps highlight that the spacecraft are
trapped within the hyperbolic tangle.
