The paper considers electromagnetic radiation arising when an instantaneous change with time of the parameters of the radiating system occurs. It is shown that under real conditions when the change in the parameters occurs in a finite time $T$, this quantity under certain conditions can be neglected and the radiation treated as the result of an instantaneous transition. Conditions are found for which this is true. As illustrations we determine the radiation fields arising on instantaneous change in magnitude and direction of a stationary point dipole moment, and also the field arising on instantaneous jump of the velocity of a point charged particle in a refracting medium.