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We study the complete process \phphbbww\ using exact matrix elementcomputations at tree-level, at a $\sqrt s=500$ GeV \eeb\ linear collider of thenext generation. Incoming photons produced via back-scattering of laser lightare considered. Sizable effects due to the finite width of the top quark aswell as to the irreducible background to $t\bar t$ production and decay arepredicted.Comment: 11 pages, Latex, 4 figures uuencoded, complete ps file available via  anonymous ftp at:  ftp://cpt1.dur.ac.uk/pub/preprints/dtp95/dtp9556/dtp9556_text.ps and  dtp9556_fig*.ps, *=1,2,3,

Finite width and irreducible background effects to $t\bar t$ production at $γγ$ Next Linear Colliders