**Abstract**

In this work, a theoretical model is developed for explanation of temporal evolution of extragalactic radio sources via beaming, orientation effects and asymmetries. Equation of the form *<sup>D</sup>* <sup>≈</sup>*P*�*<sup>q</sup>*ð Þ <sup>1</sup> <sup>þ</sup> *<sup>z</sup>* �*<sup>m</sup>* is used to account for the D � P/z relation. Also, *D* ≈ *D*<sup>0</sup> ð Þ� <sup>1</sup>þ*<sup>z</sup>* ffiffiffiffiffiffi <sup>1</sup>þ*<sup>z</sup>* <sup>p</sup> f g ð Þ <sup>1</sup>þ*<sup>z</sup>* <sup>2</sup> accounted properly for <sup>Ω</sup><sup>0</sup> <sup>¼</sup> 1 cosmology than the <sup>Ω</sup><sup>0</sup> <sup>¼</sup> 0 counterpart in linear size versus redshift of radio sources. Similarly, *<sup>D</sup>* <sup>¼</sup> *Dc* <sup>1</sup><sup>∓</sup> ln *<sup>P</sup> Pc* � � � � <sup>1</sup>*=*<sup>2</sup> h i model explained redshift-luminosity relationship of extragalactic radio sources. The results from the regression analyses are q = +0.003 (r = 0.04) for sources with z < 1 and q = �1.59 (r = �0.6) for all z≥1 sources. A critical linear size, Dc of 316kpc which matches the maximum theoretical linear size, D max of 0*:*15D0 at a critical redshift zc � 1 and a critical luminosity Pc <sup>¼</sup> <sup>26</sup>*:*33WHz�<sup>1</sup> are obtained. The indication of all these results is that the linear size of radio sources evolves up to a certain limit in D–P plane and thereafter decreases with increasing luminosity as predicted in this work.

**Keywords:** AGNs, ESS quasars, ESS galaxies, evolutions: temporal, cosmological and general
