  The standard Lorentz transformations establish a relationship between the
space-time coordinates of the same event when detected from two inertial
reference frames I and I' in the standard arrangement. This event is
characterized by the space-time coordinates E(x,tE) and E'(x',t'E), tE and t'E
representing the readings of the standard synchronized clocks C(x) and C'(x')
located in the two frames where the event takes place. We obtain the
nonstandard Lorentz transformations establishing a "physically" correct
relationship between the readings of the standard synchronized clocks and the
readings of other clocks (ta,t'a) of the same inertial reference frames. This
relationship of the type tE=f(x,ta), expresses the standard Lorentz
transformations as a function of ta and t'a respectively. We present several
cases of nonstandard Lorentz transformation (the case of radar detection, the
case when one reference frame is filled with an ideal transparent dielectric
and the case of relativity of the apparent, actual and synchronized positions
of the same moving particle).
