MADRID — Nearly 50 years ago, Inés Madrigal was taken from her parents, an unwitting participant in a scheme that started under Spanish dictator Francisco Franco’s regime as a way of removing infants from families that opposed him.

On Monday a Spanish court acknowledged a former gynecologist had played a role in the 1969 abduction of Ms. Madrigal, who was an infant at the time. It was the first case in which a doctor faced trial in Spain for what is known here as the scandal of the stolen babies. But Ms. Madrigal’s victory was, in her words, bittersweet.

The judges at a provincial court in Madrid found there was irrefutable evidence to show that Eduardo Vela, 85, was involved in the abduction of Ms. Madrigal. But they said that the charges brought against him fell under a statute of limitations, which required the charges to be filed within 10 years of Ms. Madrigal becoming an adult. This meant that Dr. Vela couldn’t be convicted of any of them.

The issue became a national scandal in 2011, when the Spanish judiciary was forced into action after Anadir, an association that represents people searching for missing children or parents, filed its first complaints.

Prime Minister Pedro Sánchez, who took over in June, is now being pressured to order a fuller accounting and offer compensation to the victims and their families.

Even though several stolen baby cases have already been closed because either the crimes were too old or those involved had died, Ms. Madrigal told local reporters that she hoped her example would encourage others.

“I’m obviously happy because they’ve recognized that Eduardo Vela did all that he did,” Ms. Madrigal told reporters outside the courtroom. But, she added, the judges in Spain should be ready to use her case as “a trampoline” and override any existing statute of limitation in cases like hers.

“There is international law concerning the forced disappearance of people — and Spain has signed onto such international law,” she added.

She also plans to take her case before the Supreme Court in Spain.

The origins of the scandal are unclear, but the practice of separating children of political opponents from their parents gathered pace after Franco won the Spanish Civil War in 1939 and sought to have the children of his Republican and far-left opponents adopted by families who espoused the Catholicism and conservative nationalist ideology of his regime.

Prosecutors have claimed that the abductions were facilitated by representatives both of the medical profession and of the Catholic clergy, at a time when nuns worked in maternity hospitals and ran many of Spain’s orphanages.

As part of an earlier and broader investigation into the crimes ensuing from the civil war, Judge Baltasar Garzón had estimated that as many as 30,000 children were abducted under Franco.

Franco’s regime lasted from 1939 until his death in 1975, when what may have begun as political retaliation toward leftist families appears to have mutated into a trafficking business that continued after the dictator’s death and in which doctors, nurses and also nuns colluded with criminal networks.

María Gómez Valbuena, a nun known as Sister María, became the first person to be indicted in such a case. She was accused in 2012 by a woman, María Luisa Torres, of participating in the abduction of her child, who was born in a Madrid hospital in 1982.

The nun denied wrongdoing, refused to appear before the judge because of her ill health and then died in 2013 — but not before being accused by others of perpetrating similar crimes.

When she turned 18, Ms. Madrigal was told by her mother that she had been adopted. She eventually accused Dr. Vela of forging her birth certificate so that it showed her adoptive mother, who died two years ago, as her biological parent.

Dr. Vela, a former director at the San Ramón clinic in Madrid, was charged with crimes that included abduction and document forgery. He faced a prison term of up to 11 years.

Dr. Vela denied wrongdoing in late 2013, when he first appeared in court in connection with the case. Asked why his name appeared on Ms. Madrigal’s fake birth certificate, he told the court that he had been “signing things without looking at them.”

More recently, Dr. Vela’s lawyers said that his deteriorating health prevented him from making further court appearances and sought to have the case postponed indefinitely. He was not present when the decision was announced on Monday.

Since taking over earlier this year, Mr. Sánchez has promised to revive a law of historical memory that addresses injustices committed during and after the Civil War. The law finances the identifying of thousands of victims of the civil war who were dumped into mass graves, renaming streets and squares that still honor participants in the dictatorship, and other similar measures.

Last month, Mr. Sánchez also earned support in Parliament for his plan to exhume Franco’s remains from the giant underground basilica that the dictator had built after winning the war.

Antonio Barroso, the president of Anadir, said in an interview Monday that Mr. Sánchez and his new Socialist government should open a full investigation into the missing infants and treat them “like any other victims of Franco deserve to be treated.” That treatment, he said, should include financial compensation.

The case of Dr. Vela only confirms what’s been known for some time: that “many people stole many babies,” said Mr. Barroso, who is himself a victim of this scheme.

He founded Anadir in 2010 after himself discovering that he had been adopted. Mr. Barroso took DNA samples from the woman he had always known as his mother and confronted her after tests showed that the samples did not match. She admitted paying a nun for a baby and misleading her son about his birth for decades.

“We’ve spent years talking to government officials and dealing with judges who have made every possible effort to make sure nothing more comes out of this scandal,” Mr. Barroso said. “It ’s now more than time to change that.”