[en] The main features and limits of present and future indirect searches of one extra neutral Z of general theoretical origin are overviewed. At the end of the LEP and of the pp collider runs, negative searches of a Z' will force this particle to be characterized in general by a high (more than ∼5-6 TeV) mass and by a very low mixing angle in orthodox cases. These negative features might lead to severe restrictions on the candidate models and, possibly, to a deeper theoretical understanding of their origin. (R.P.) 16 refs., 7 figs