Hydrogen bonding (HB) in a system consisting of A(a)D(d) type molecules is studied by two different statistical ways that are demonstrated to be consistent with each other. The free energies of the sol and gel phases in both pregel and postgel regimes are further obtained. It is shown that the sol-gel phase transition in a non-linear HB system is a geometrical phase transition, and for describing this phase transition, the scaling laws satisfied by the moments, the radii of gyration and the gel free energy near the critical point are obtained. (c) 2005 Elsevier B.V. All rights reserved.