Abstract: The discovery of TeV gamma-ray emission of BL Lac objects (a class of active galactic nuclei dominated by non-thermal emission) gave new insights into the particle acceleration and the emission processes in the highly relativistic jets. In order to shed light on these processes, the spectral energy distribution (SED) of sources with different characteristics has been studied in details. BL Lac objects with exceptional TeV spectra, i.e. with extreme values for the spectral index, have been selected. In addition, sources with different maximum energies in the SED cover the different sub-classes of BL Lac objects. The basic aim was to study with new, simultaneous multi-wavelength observations in the optical, UV, X-ray, GeV and TeV gamma-ray regime, if the emission processes of these extreme cases of TeV BL Lac objects can be explained by the synchrotron Self-Compton model, which is well established for the class of BL Lac objects at lower energies. During this study, a clear extended non-thermal X-ray jet in AP Librae was detected. This was surprising, since X-ray jets are unusual for TeV emitting BL Lac objects.