Starting on positive trajectories at school entry is important for children's later academic success. Using partial least squares, we sought to specify interrelations among all theory-based components of social-emotional learning (SEL), and their ability to predict later classroom adjustment and academic readiness in a modelling context. Consequently, self-regulation, emotion knowledge, social problem solving, and social-emotional behaviour were assessed via direct assessment and observation for 101 preschoolers; teachers provided information on classroom adjustment through kindergarten and academic readiness in kindergarten. Our final outer (measurement) model showed robust latent variables for SEL components. Regarding the inner (structural) model, latent variables showed expected predictive relations among SEL components, and with later classroom adjustment and academic readiness: preschoolers' executive control predicted aspects of their social cognition (i.e., emotion knowledge and social problem solving) and emotionally negative/aggressive behaviour, and emotion knowledge predicted their emotionally regulated/prosocial behaviour. Further, most SEL components directly and/or indirectly predicted teachers' evaluations of later classroom adjustment and kindergarten academic readiness. Our findings extend our understanding of SEL during preschool, suggesting that early assessment and monitoring is possible using these instruments, and potentially aiding the development of programmes to maximize children's SEL in the service of early school success.