The incidents listed in Penn's alert took place between 4:30 p.m. and 12:30 a.m., in these areas: 33rd and Chestnut streets, Locust Street near 40th and near 42nd, and Locust Walk near 37th Street.
A similar incident also occurred at 35th and Spring Garden streets, in the vicinity of Drexel University, the alert said.
The youths involved were all male, up to 13 years old, and walked the campus area in groups of three to eight, according to the alert, which was issued late last week.
Two youths have been arrested in connection with one of the incidents, on Locust Street near 42nd.
Patrols have been stepped up in the area, including covert operations, and security cameras were being monitored. City police and safety personnel from the University City District also are involved in the investigation.
The university began installing more closed-circuit cameras and emergency phones early last year, after a student was hit in the thigh by a stray bullet during an aborted robbery and a man was killed in a diner just off campus on Christmas Day 2005.
A Drexel graduate student was severely beaten by four University City High School students in January 2006 at 36th and Spring Garden streets.