  Electromagnetic properties of off-shell particles are discussed on the basis
of a purely electromagnetic reaction: virtual Compton scattering off a proton.
It is shown that the definition of off-shell electromagnetic form factors is
not gauge invariant and that these cannot be investigated in practice. Using
only fundamental requirements of gauge invariance it is demonstrated that
off-shell effects are cancelled in the longitudinal components of the total
conserved current by the minimal contact current, while the off-shellness
appears only in the the transverse (gauge invariant) non-pole part. This
provides the possibility to introduce an on-shell extrapolated form factor
F_1^+(q^2) in a gauge invariant way for the unphysical time-like region,
4m_e^2<q^2, 4M_N^2.
