PARIS -- Freezing fog and light snow had closed in over northern France when the Calais-Riviera night train began its journey on Dec. 13 with fewer than 60 people aboard. Among the passengers was a murderer with a knife.

Less than three hours later, he had stabbed Corinne Caillaux 13 times while her 6-year-old son lay sleeping. Long before her body was found, the man police call the "corridor killer" had stepped off the train and escaped in the darkness.Since that killing, reports have emerged of a trail of attacks on lone women traveling at night.

Police are searching for the chief suspect, Ahmed Sid Rezala, even as questions are being raised about the effectiveness of French police.

Rezala had drawn attention to himself because he showed his identity card, complete with his name and address, to 42 ticket inspectors who issued him with written summonses for failing to pay his fare.

Described by probation officers as "unstable and dangerous with a liking for knives," Rezala is believed to have been on the train when Peake was murdered. A witness had seen him talking to the British student as she waited for the Paris-bound express. Rezala was again caught dodging his fare on the Calais-to-Riviera train on which Caillaux, 36, was murdered.

Police are watching the Rezala family's house in Marseilles in hopes of catching the suspect. Rezala returned there last Wednesday and then slipped away unseen.

Meanwhile, another man with a record of criminal violence is also reported to have been caught repeatedly traveling without a ticket on night trains. Worries over which suspect carried out the murders should be resolved when DNA tests are finished on a bloodstained baseball cap found near Caillaux's body.

(Distributed by Scripps Howard News Service. For more Observer news go to http://www.guardian.co.uk/.)