The 6-year-old girls' uncle, Dr. Valerio Lucidi, told reporters outside their home in a suburb of Lausanne that every passing minute is filled with fear.
He said hopes had dimmed since the police discovered that the girls' father - and presumed custodian - had withdrawn ¿7,000 ($9,570) in the French port of Marseille last week and mailed ¿4,400 of it to Lucidi's sister, Irina Lucidi.
Lucidi said this suggests Schepp did not intend using the money to provide care for Alessia and Livia.
"This worries us a lot that we received the money because it shows there is no caregiver," said the Belgian surgeon. "We are really scared that something bad happened."
Schepp also sent his wife a note from Marseille saying he could not live without her, and a letter a day later from nearby Toulon.
Schepp's body was found last Thursday in southern Italy with about ¿100. Police say they believe he threw himself under a train.
Swiss police late Tuesday confirmed some of his last movements.
They said Schepp, who was spending the weekend with his daughters, was last known to have been with them on Sunday, Jan. 30, around 1 p.m. Lucidi had told reporters that was when the girls were playing with a neighbor's child.
The police said Schepp's mobile phone showed he was in nearby Morges about 2 1/2 hours later.
From there, they said, he went to Geneva and crossed over the border into France in the Annecy region shortly after 6 p.m. that night.
He was supposed to return the girls to their mother's house or to school the next day in Lausanne's lakefront community of St. Sulpice, where both parents lived.
That night, their mother, a senior legal counsel with Philip Morris International in Lausanne, alerted police that the girls were missing after exchanging puzzling text messages with Schepp, who also worked at the tobacco giant.
French police established that Schepp took the ferry Sunday night from Marseille to Propriano, on the Mediterranean island of Corsica, where a witness recounted seeing him on Tuesday, Feb. 1. From there, he went to Naples in Italy.
Schepp's black Audi A6 was found Thursday in Cerignola, where his body was also discovered.
It remains uncertain whether the girls were with him after Lausanne. In Marseille, he bought three ferry tickets to go to Corsica, but police said there is no evidence they were used.
"I hope we will find them as soon as possible but our hope is diminishing minute after minute," said Lucidi. He added that the twins are "very bright," fluent in French and Italian, and capable of fending for themselves, if necessary.
Over the past few days, the hunt in St. Sulpice has intensified to focus on a lake, boats in nearby towns, and gas stations between Lausanne and Geneva, about 50 kilometers (31 miles) away, that may have been used by the father.
Some 40 Swiss investigators are working on the case. Police have gone door-to-door in St. Sulpice interviewing dozens of residents and searched both parents' homes repeatedly for clues.
Police are seeking eyewitnesses who may have seen the girls since they went missing more than a week ago.
Both girls are blond and wear glasses. Alessia was dressed in blue jeans, a striped T-shirt and white jacket; Livia wore a purple ski jacket with white and pink sneakers.