Emotion socialization by parents contributes to children's trajectories of healthy and unhealthy emotional development, but there has been little research into the determinants and development of parental emotion socialization. We examined whether young children's anxious characteristics, including expressed anxiety with peers and low basal respiratory sinus arrhythmia (RSA), predicted changes in mothers' and fathers' emotion socialization over the subsequent year. Using regression and regions of significance analyses, we observed that children's expressed anxiety moderated the stability of mothers' and fathers' supportive and unsupportive emotion socialization, primarily in ways that would be likely to maintain or exacerbate children's social anxiety. For example, mothers' highly fretful and less supportive responses were more stable when children had been more anxious with peers. Basal RSA moderated the stability of fathers' punitive responses to children's anxious and sad emotions, and directly predicted changes in mothers' neglect of children's anxious and sad emotions, and negative and positive feelings about children's social withdrawal. These effects of children's characteristics on parents' emotions and behaviors support bidirectional and transactional models of the socialization of children's anxiety and internalizing problems, and identify aspects of emotion socialization by parents that could be amenable to intervention.