The trial opened on Sunday was adjourned for several months because several of the accused were absent.
Most of the accused had not been detained and the five who did not appear all live in France and have double nationality.
The princiapal accused, according to Algerian paper Réflexion, is alleged to have posed as an obstetrician and set up a clinic in Ain Taya, near Algiers, and, with the aid of his sister, set up a child-trafficking network in the 1990s.
They paid young, single pregnant women to sell their babies at birth and then sold them to families, mainly in France, using falisified birth certificates provided by notaries who were in on the plot.
The children were taken to Saint Etienne in central France and given up for adoption in return for money.
The principal accused claims that the mothers agreed to the scheme but several say they threatened and forced to give up their babies.
He is also accused of illegal abortions and of keeping the foetuses to sell in France.
The child-trafficking network came to light in 2009, when a young woman died during an abortion.