Activity of many physiological subsystems has a well-expressed rhythmic character. Often, a dependency between physiological rhythms is established due to interaction between the corresponding subsystems. Traditional methods of data analysis allow one to quantify the strength of interaction, but not the causal interrelation that is indispensable for understanding the mechanisms of interaction. Here we present a recently developed method for quantification of coupling direction and apply it to an important problem. Namely, we study the mutual influence of respiratory and cardiovascular rhythms in healthy newborns within the first six months of life in quiet and active sleep. We find an age related change of the coupling direction: the interaction is nearly symmetric during the first days, and becomes practically unidirectional (from respiration to heart rhythm) at the age of six months. Next, we show that the direction of interaction is mainly determined by respiratory frequency. If the latter is less than 0.6 Hz, the interaction occurs dominantly from respiration to heart. With higher respiratory frequencies that only occur at very young ages, the dominating direction is less pronounced or even abolished. The observed dependencies are not related to sleep stage, suggesting that the coupling direction is determined by system inherent dynamical processes, rather than by functional modulations. The directional analysis may be applied to other interacting narrow band oscillatory systems, e.g. in the central nervous system. Thus, it is an important step forward in revealing and understanding causal mechanisms of interactions.