Theoretical investigation of properties of assumed gene networks constructed from elementary units of two types, genetic elements and control links, was carried out. A test was formulated for a subclass of such networks with cyclic structure called S(n,k)-networks allowing calculation-free prediction of the network limiting properties (the presence/absence and number of stationery and/or cyclic functioning modes) from a graph of the network structure. The obtained data can be useful for constructing gene networks with predefined properties.