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.