There has been longstanding interest in the evolution of positive and negative relationships among countries. An interdisciplinary field of study, Structural Balance Theory, has developed on the dynamics of such appraisal systems. However, the advancement of research in the field has been impeded by the lack of longitudinal empirical data on large-scale networks. We construct the networks of international amicable and hostile relations occurring in specific time-periods in order to study the global evolution of the network of such international appraisals. Here we present an empirical evidence on the alignment of Structural Balance Theory with the evolution of the structure of this network, and a model of the probabilistic micro-dynamics of the alterations of international appraisals during the period 1995-2018. Also remarkably, we find that the trajectory of the Frobenius norm of sequential transition probabilities, which govern the evolution of international appraisals among nations, dramatically stabilizes.