  The period-luminosity relations (PLR) of Milky Way $\delta$ Scuti ($\delta$
Sct) stars have been described to the present day by a linear relation.
However, when studying extragalactic systems such as the Magellanic Clouds and
several dwarf galaxies, we notice for the first time a non-linear behaviour in
the PLR of $\delta$ Sct stars. Using the largest sample of $\sim 3700$
extragalactic $\delta$ Sct stars from data available in the literature
$-$mainly based on OGLE and SuperMACHO survey in the Large Magellanic Cloud
(LMC)$-$ we obtain that the best fit to the period-luminosity ($M_V$) plane is
given by the following piecewise linear relation with a break at $\log{P} =
-1.03 \pm 0.01$ (or $0.093 \pm 0.002$ d) for shorter periods (sp) and longer
periods (lp) than the break-point: $$M_V^{sp} = -7.08 (\pm 0.25) \log{P} -5.74
(\pm 0.29) ;\hspace{5pt} \log{P} < -1.03$$ $$M_V^{lp} = M_V^{sp} + 4.38 (\pm
0.32) \cdot (\log{P} + 1.03 (\pm 0.01));\hspace{5pt} \log{P} \geq -1.03$$
Geometric or depth effects in the LMC, metallicity dependence, or different
pulsation modes are discarded as possible causes of this segmented PLR seen in
extragalactic $\delta$ Sct stars. The origin of the segmented relation at $\sim
0.09$ days remains unexplained based on the current data.
