  We analyze how the spectrum of synchrotron and inverse Compton radiation from
a narrow relativistic jet changes with the observation angle. It is shown that
diversity of acceleration mechanisms (in particular, taking the converter
mechanism (Derishev et al. 2003) into account) allows for numerous
modifications of the observed spectrum. In general, the off-axis emission in
GeV-TeV energy range appears to be brighter, has a much harder spectrum and a
much higher cut-off frequency compared to the values derived from Doppler
boosting considerations alone. The magnitude of these effects depends on the
details of particle acceleration mechanisms, what can be used to discriminate
between different models.
  One of the implications is the possibility to explain high-latitude
unidentified EGRET sources as off-axis but otherwise typical relativistic-jet
sources, such as blazars. We also discuss the broadening of beam pattern in
application to bright transient jet sources, such as Gamma-Ray Bursts.
