Disturbances in cerebral hemodynamics are one of the principal causes of cerebral damage in premature infants. Specifically, changes in cerebral blood flow might cause ischemia or hemorrhage that can lead to motor and developmental disabilities. Under normal circumstances, there are several mechanisms that act jointly to preserve cerebral hemodynamics homeostasis. However, in case that one of these mechanisms is disrupted the brain is exposed to damage. Premature infants are susceptible to variations in cerebral circulation due to their fragility. Therefore, monitoring cerebral hemodynamics is of vital importance in order to prevent brain damage in this population and avoid subsequent sequelae. This thesis is oriented to the development of signal processing techniques that can be of help in monitoring cerebral hemodynamics in neonates.There are several problems that hinder the use in clinical practice of monitoring cerebral hemodynamics. On one hand, continuous measurements of cerebral blood flow, or hemodynamical variables, are difficult to obtain in premature infants. In this context, Near Infrared Spectroscopy (NIRS) is one of the few technologies that is available for the measurement of hemodynamical variables in this population. NIRS is a noninvasive and safe technology that is based on light radiation. NIRS allows the continuous measurement of cerebral oxygenation that under certain considerations reflects changes in cerebral blood flow. On the other hand, cerebral hemodynamics assessment is performed by evaluating the strength of the relationship between some systemic variables, e.g. mean arterial blood pressure and concentration of CO2, and the cerebral hemodynamics variables. Under normal conditions cerebral hemodynamics variables should be independent of systemic variations. Coupled dynamic between systemic and cerebral hemodynamics variables represents a high risk situation for the patient. Among the techniques available for the monitoring of cerebral hemodynamics, most of them assume that the mechanisms responsible for its control are linear and univariate. In reality, these mechanisms are nonlinear, multivariate, nonstationary and highly coupled.This thesis, on one hand, introduces the use of more sophisticated signal processing techniques for monitoring cerebral hemodynamics, which can address the multivariate and/or the nonlinear nature of the mechanisms involved in its control. Linear techniques such as canonical correlation analysis, subspace projections and wavelet based transfer function; and nonlinear techniques such as least squares support vector machines and kernel principal component regression, have been introduced for the NIRS-based monitoring of cerebral hemodynamics. On the other hand, kernel principal component regression is a nonlinear methodology that produces as result a black box model, which lacks clinical interpretability. Therefore, in this thesis attention has been given to the development of methodologies that allow to interpret the results produced by this nonlinear model in a clinical framework. For this purpose a method based on subspace projections is proposed. In addition, in this thesis, results from several clinical studies related to monitoring cerebral hemodynamics are presented.