LOS ANGELES — Their bodies were dumped in alleys and garbage bins in South Los Angeles, some naked, some covered with mattresses and trash. Most had been shot in the chest after some type of sexual contact, others strangled.

As prosecutor Beth Silverman showed photo after photo of the 10 victims to a packed courtroom on Tuesday, family members of the dead young women shook as they wept. Some covered their faces, others had to walk out.

It was an emotional beginning to the long-awaited ‘‘Grim Sleeper’’ trial more than 30 years after the first victim’s death.

Lonnie Franklin Jr. has pleaded not guilty to killing nine women and a 15-year-old girl between 1985 and 2007 in one of the city’s most notorious serial killer cases. Franklin, 63, has been behind bars awaiting trial for nearly six years since his arrest in 2010.

The ‘‘Grim Sleeper’’ nickname was coined because of an apparent 14-year gap in the murders between 1988 and 2002.

Police have dueling theories about the gap. Some think the killings stopped after one intended victim survived in 1988, scaring off the attacker. Other investigators believe there were more victims but their bodies just weren’t found.

In her opening statement to jurors, Silverman said Franklin took advantage of the crack cocaine epidemic in South Los Angeles, targeting women ‘‘willing to sell their bodies and their souls in order to gratify their dependency on this powerful drug.’’

Autopsies showed all but one victim had cocaine in their systems when they were killed. Some had turned to prostitution.

‘‘This was the perfect opportunity for someone who preyed on women,’’ Silverman said. ‘‘Someone who knew the streets and the dark alleys by heart, someone who lived there and was able to blend in, someone who knew where the drug-addicted women and perhaps prostitutes would congregate and who knew how to lure potential victims into the darkness and the isolation of a vehicle through the promise of crack.’’

Franklin’s attorney Seymour Amster will deliver his opening statement later in the trial.

‘‘There’s more to it than people want to believe,’’ Amster said last week.

Silverman said the killings all were linked by firearms or DNA that matched Franklin. She also showed jurors photos that Franklin had in his home of two victims, including one who had just been shot in the chest when she was photographed.

As many as 30 detectives investigated the Grim Sleeper killings in the 1980s. They exhausted leads within a few years.

A special squad of detectives was assembled after the most recent killing, the June 2007 shooting of 25-year-old Janecia Peters, whose naked body was found in the fetal position inside a trash bag.

Police arrested Franklin three years later after his DNA was connected to more than a dozen crime scenes. An officer posing as a busboy at a pizza parlor got DNA samples from dishes and utensils Franklin had been using at a birthday party.

Family members of the Grim Sleeper victims and a survivor of the attacks have been frustrated by repeated delays in the case and were eager for the trial to start.

Porter Alexander, the father of one of the victims, was 48 when his 18-year-old daughter was killed. He’s now 75.

‘‘The day of reckoning is here,’’ Alexander said last week. ‘‘You can’t help but be excited that you lived to see an end to this madness. It’s been a long road, and I'm glad I'll physically be able to be there.’’

When photos of his daughter’s naked body were shown in court Tuesday, Alexander walked out as other family members comforted his weeping wife.

The Grim Sleeper was among at least three serial killers who stalked Los Angeles-area women during the crack cocaine epidemic in the 1980s and 1990s.

The attacks were dubbed the ‘‘Southside Slayer’’ killings before authorities concluded more than one attacker was involved.