With the increased survival of very preterm infants, there is a growing concern for their developmental outcomes. Infant cry characteristics reflect the development and possibly the integrity of the central nervous system. In this paper, relationships between fundamental frequency (F(0)) and vocal tract resonance frequencies (F(1)-F(3)) are investigated for a set of preterm newborns, by means of a multi-purpose voice analysis tool (BioVoice), characterised by high-resolution and tracking capabilities. Also, first results about possible distress occurring during cry in preterm newborn infants, as related to the decrease of central blood oxygenation, are presented. To this aim, a recording system (Newborn Recorder) has been developed, that allows synchronised, non-invasive monitoring of blood oxygenation and audio recordings of newborn infant's cry. The method has been applied to preterm newborns at the Intensive Care Unit, A.Meyer Children Hospital, Firenze, Italy.