  We study the chaotic behavior of the ``GOY'' shell model by measuring the
variation of the maximal Lyapunov exponent with the parameter $\epsilon$ which
determines the nature of the second invariant (the generalized ``helicity''
invariant). After a Hopf bifurcation, we observe a critical point at
$\epsilon_c \sim 0.38704$ above which the maximal Lyapunov exponent grows
nearly linearly. For high values of $\epsilon$ the evolution becomes regular
again which can be explained by a simple analytic argument. A model with few
shells shows two transitions. To simplify the model substantially we introduce
a shell map which exhibits similar properties as the``GOY'' model.
