This is the first of a series of papers on the application of Wertheim’s multidensity formalism to study the connectivity and related properties of equilibrium polymerizable particles. We first consider in detail the case in which each monomer has two sites available for covalent bonding. We modify Wertheim’s treatment to apply it to the case where the two sites on a monomer are indistinguishable, i.e., to homofunctional units. A study is presented of the connectedness behavior in these systems, including expressions for the weight-average molecular weight and cluster size. The application of these results to specific models is reported in subsequent parts of this series.