local slope of the $\sigma_{p}$ does not stop increasing in the GOY model, even though this is hardly perceptible to the eye. Also significant is the lack of convergence for $p\geq 8$. We note that the points marking the upper error bars, which were obtained from one particular run among six of equal temporal length, are surprisingly well fitted by the formula proposed by She and Leveque [@SL] for real Navier-Stokes turbulence $$\sigma_{p}=\frac{2p}{9} -2[1-(\frac{2}{3})^{p\over 3}]
\label{SheLev}$$ up to the highest values of $p$ investigated here. A physical reason for this good agreement observed by many others is missing. We did not try to tighten our error bars by increasing the length of numerical integration since this was beyond the scope of this work. The results of the next Section will somehow confirm the peculiar nature of intermittency in the GOY model for such values of parameters as $\epsilon =0.5$ and $Q=2$.\

Study of self-similar solutions
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Let us take for granted from the results of the preceding Section that the scaling exponents $\sigma_{p}$ grow asymptotically like $\gamma p$ at large $p$, with $\gamma $ a positive number depending on the parameter $\beta $ only. This means that the amplitude of 