The effect of interfacial characteristics on the effective thermal conductivity, k(eff), of isotropic two-dimensional periodic composites of infinitely long circular cylinders is studied with a boundary collocation scheme. Three types of problems are investigated : coated inclusion, debonded inclusion and contact resistance problems. It is shown that a critical relative interfacial layer thickness, (delta/a)(c), exists for the first two problems, at which the insulating or conducting effect of the inclusion is exactly balanced out by that of the interfacial layer such that no effect of inclusion addition can be realized. The expression for the critical relative interfacial layer thickness is derived and studied. For the third problem, the contact resistance is characterized by the Blot number, and a critical Blot number is found to exist and its expression is also derived. The second problem is further shown to reduce to the third problem for composites with thin debonding layer, A thorough parametric study is then conducted for the effective thermal conductivity subject to various system parameters including the reduced thermal conductivities of the inclusion (sigma(2)) and interfacial layer (sigma(3)), the relative interfacial layer thickness (delta/a), the Blot number (Bi), the total inclusion volume fraction (f), and the microstructure (square or hexagonal arrays). The parameter domains investigated are either complete or widely ranged to cover most practically realizable systems. Two new independent parameters, (delta/a) sigma(3) and (Bi) sigma(2), are identified for the coated inclusion and contact resistance problems, respectively, when the composites are not heavily loaded. Their physical implications are discussed and their effects on k(eff) are studied. It is found that composites with contact resistance characterized by Bi can be viewed as composites of no contact resistance but with cr, replaced by (Bi) sigma(2), for the calculation of k(eff) when sigma(2) > 10 and Bi < 0.1. The effect of various parameters on the effect of interfacial characteristics is also investigated. The interfacial effect becomes more pronounced with increasing total inclusion volume fractions, and is more revealing for square arrays.