The present work is motivated by our recent experimental results 2-4 that indicate on anomalously small retardation of bound (or velocity-dependent) electromagnetic (EM) fields in the near zone of an emitter, whereas in the far zone the retardation tends to the standard value determined by the velocity of light c. Such anomaly is specific only for bound field component, while EM radiation has the constant propagation velocity c in the entire space. One possible explanation of these experimental results can be linked to our earlier finding 6, 8 that conventional EM energy-momentum (EMEM) tensor describes bound and radiative EM fields only in spatial regions free of charges and currents. In this work we show that an additional term has to be included into the standard EMEM tensor in order to make viable the description of the whole system of "charges plus fields". Such approach to the EMEM tensor actually admits anomalously small retardation of bound EM fields in regions very close to a field source, providing the standard propagation in the far zone. Some special implications are also discussed.