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We study the phase structure of nonlocal two dimensional generalized Yang -Mills theories (nlgYM$_2$) and it is shown that all order of $\phi^{2k}$ modelof these theories has phase transition only on compact manifold with $g = 0$(onsphere), and the order of phase transition is 3. Also it is shown that the$\phi^2 + \frac{2\alpha}{3}\phi^3$ model of nlgYM$_2$ has third order phasetransition on any compact manifold with $1 < g < 1+ \frac{\hat{A}}{|\eta_c|}$,and has no phase transition on sphere.Comment: 11 pages, no figure

MORE ON PHASE STRUCTURE OF NONLOCAL 2D GENERALIZED YANG–MILLS THEORIES (nlgYM2's)

MORE ON PHASE STRUCTURE OF NONLOCAL 2D GENERALIZED YANG–MILLS THEORIES (nlgYM₂'s)