  The relativistic theories of light propagation are generalized by introducing
two new parameters $\varsigma$ and $\eta$ in the second post-Newtonian (2PN)
order, in addition to the parameterized post-Newtonian parameters $\gamma$ and
$\beta$. This new 2PN parameterized (2PPN) formalism includes the
non-stationary gravitational fields and the influences of all kinds of
relativistic effects. The multipolar components of gravitating bodies are taken
into account as well at the first post-Newtonian order. The equations of motion
and their solutions of this 2PPN light propagation problem are obtained.
Started from the definition of a measurable quantity, a gauge-invariant angle
between the directions of two incoming photons for a differential measurement
in astrometric observation is discussed and its formula is derived. For a
precision level of a few microacrsecond ($\mu$as) for space astrometry missions
in the near future, we further consider a model of angular measurement,
LATOR-like missions. In this case, all terms with aimed at the accuracy of
$\sim1\mu$as are estimated.
