its behaviour in recent publications [@BBP; @BLLP; @KLWB] (we shall go back to some of these results in the bulk of the paper).\
The GOY model uses complex velocity variables and interactions among all triads made up of three different neighbouring shells. One may wonder whether these two features are necessary to produce “good” chaotic properties. In order to clarify this question, we report in this paper a mostly numerical investigation of the scaling properties of a simpler class of shell models, which results from the linear superposition of two chains introduced in the early $70'$s by Obukhov [@O] and Novikov [@DN] (for an historical insight into the field and a comprehensive review of the huge russian litterature concerned with cascade-like systems under various disguises, see for instance [@GGO]). In the Obukhov-Novikov model, hereafter referred to as the ON model, the velocity variables are real and interacting triads involve only two neighbouring shells. The structure of non-linearities depends as in the GOY model on a single parameter (together with the scale parameter $Q$), which fixes in that case the relative proportion of the two basic chains. Both models exhibit qualitatively the same phenomenology. When the proportion of Novikov-like interactions (favouring 