Preterm infant neuronal development is related to the distribution of their sleep states. The distribution changes throughout development. Automated sleep state monitoring can become a powerful aid for development monitoring in preterm infants. Three datasets including 34 preterm infants and a total of 18,018 30 s manually annotated sleep intervals (sleep-epochs) were analyzed in this study. The annotation of sleep states includes active sleep, quiet sleep, intermediate sleep, wake, and caretaking. Four different recurrent neuronal network architectures were compared for two-state, three-state, and all-state analysis. A sequential network was used to compare long- and short-term memory and gated recurrent unit models. The other network architectures were based on the popular ResNet and ResNext architectures utilizing residual connection for more depth. The most essential sleep states, active and quiet sleep, could be separated with a kappa of 0.43 ± 0.08. Quiet versus caretaking and wake showed a kappa of 0.44 ± 0.01. The three state classifications of active versus quiet versus intermediate sleep resulted in a kappa of 0.35 ± 0.07 and active versus quiet versus wake and caretaking resulted in a kappa of 0.33 ± 0.04. The all-state classification was underperforming with probably due to difficulty in separating subtle differences between all states and a lack of sufficient training data for the minority classes.