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We analyze the $1/\theta$ and 1/N expansions of the Wilson loop averages$<W(C)>_{U_\theta (N)}$ in the two-dimensional noncommutative $U_\theta (N)$gauge theory with the parameter of noncommutativity $\theta$. For a genericrectangular contour $C$, a concise integral representation is derived(non-perturbatively both in the coupling constant $g^{2}$ and in $\theta$) forthe next-to-leading term of the $1/\theta$ expansion. In turn, in the limitwhen ${\theta}$ is much larger than the area $A(C)$ of the surface bounded by$C$, the large $\theta$ asymptote of this representation is argued to yield thenext-to-leading term of the $1/\theta$ series. For both of the expansions, thenext-to-leading contribution exhibits only a power-like decay for areas$A(C)>>\sigma^{-1}$ (but $A(C)<<{\theta}$) much larger than the inverse of thestring tension $\sigma$ defining the range of the exponential decay of theleading term. Consequently, for large $\theta$, it hinders a direct stringyinterpretation of the subleading terms of the 1/N expansion in the spirit ofGross-Taylor proposal for the $\theta=0$ commutative D=2 gauge theory.Comment: LaTex, 50pp., 9 PostScript figure

Wilson loops in 2D noncommutative euclidean gauge theory: 2. 1/θ expansion