  The Strong Equivalence Principle (SEP) demands, besides the validity of the
Einstein Equivalence Principle, that all self-gravitating bodies feel the same
acceleration in an external gravitational field. It has been found that metric
theories of gravity other that than general relativity typically predict a
violation of the SEP. In case of the Earth-Moon system (weak field system) this
violation is called the Nordtvedt effect. It has been shown by Damour and
Sch\"afer, that small-eccentricity long-orbital-period binary pulsars with a
white dwarf companion provide excellent conditions to test the SEP in strong
field regimes. Based on newly discovered binary pulsars this paper investigates
a possible violation of the SEP in strong field regimes. New limits with an
improved confidence level are presented. The results of this paper lead to
constrains on the combination $\epsilon/2-\zeta$ of the only two
(post)$^2$-Newtonian parameters $\epsilon$ and $\zeta$ that arise from the
(post)$^2$-Newtonian approximation of the tensor-multi-scalar theory of Damour
and Esposito-Far{\`e}se.
