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Our aim in this paper is to recall some essential points of "Extended specialRelativity", now more correctly called "Non-Restricted special Relativity"theory (NRR), and in particular of the extended Maxwell Equations; as well asto set forth some further comments on the basic differences between CherenkovRadiation and the so-called X-shaped Waves, met within the more recent realm ofthe Non-diffracting Waves (also known as Localized Waves). The occasion isfurnished by some very recent Seshadri's comments[1] on a previous article ofours, titled "Cherenkov radiation versus X-shaped localized waves" (see[2], andarXiv:0807.4301[physics.optics]), and not less on NRR itself.  OCIS codes: 320.5550; 350.7420; 070.7345; 350.5500; 070.0070; 100.7410;050.050; 000.1600; 000.2690; 000.6800; 250.5530; 260.0260.  PACS nos.: 41.60.Bq; 03.50.De; 03.30.+p; 41.20;Jb; 04.30.Db; 42.25.-p;42.25.Fx; 47.35.Rs.  Keywords: Non-diffracing Waves; Localized Waves; Cherenkov radiation;X-shaped waves; Wave equations; Bessel beams; Superluminal pulses; Maxwellequations; Special Relativity; Non-restricted Special Relativity; Extendedspecial Relativity; Lorentz transformations; Superluminal point-charges.

On the "Non-Restricted special Relativity" theory (NRR), and further comments on "Cherenkov vs X-waves"