A mean-field theory of phase equilibria in solutions of semiflexible telechelic polymers is presented. All functional groups at the ends of telechelic chains are assumed to be associated in a-fold and 3-fold aggregates. It is shown that with a nonzero probability of 3-fold aggregation, infinite cluster (reversible network) formation always occurs as a first-order transition, implying an equilibrium between a gas of small rings and a network. of finite density, mixed with rings. The phase-separation region is narrow if the effective energy of a 3-fold cross-link is high enough, but it might be also very wide (implying a large ratio of network volume fraction to that of rings in coexisting phases) if the cross-links are favorable. In the latter case clusters of three telechelic chains (triplets) might become more favorable than rings; more complex finite clusters are never important.