Following the discovery of high-energy (HE; $E>10,{rm MeV}$) and very-high-energy (VHE; $E>100,{rm GeV}$) $gamma$-ray emission from the low-frequency-peaked BL~Lac (LBL) object AP Librae, its electromagnetic spectrum is studied over 60 octaves in energy. Contemporaneous data in radio, optical and UV together with the $gamma$-ray data are used to construct the most precise spectral energy distribution of this source. The data have been found to be modeled with difficulties with single zone homogeneous leptonic synchrotron self-Compton (SSC) radiative scenarios due to the unprecedented width of the high-energy component when compared to the lower-energy component. The two other LBL objects also detected at VHE appear to have similar modeling difficulties. Nevertheless, VHE $gamma$ rays produced in the extended jet could account for the VHE flux observed by H.E.S.S.
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