A Navarra Hospital statement said one Spaniard was hospitalized for injuries to the ribs while a Frenchman was treated for multiple bruises but later released.
No one was gored, making it a relatively clean run lasting 2 minutes, 14 seconds.
Two Americans and a Briton were gored and eight others injured in the first run yesterday. All but two Americans were released the same day.
One American still hospitalized was Mike Webster, a 38-year-old occupational therapist from Gainesville, Florida, who was gored in the armpit as he joined the bull-run in Pamplona for the 38th time in 11 years. He said yesterday he hadn't decided whether he'd run again.
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The nationally televised 8 am run sees people racing with six bulls and their guiding steer along a narrow 850-metre course from a holding pen to the city bull ring. The bulls are then killed by professional matadors in bullfights each afternoon.
The nine-day fiesta in Pamplona, which features 24-hour street partying, was made famous in Ernest Hemingway's 1926 novel "The Sun Also Rises" and attracts thousands of foreign tourists.
Bull runs are a traditional part of summer festivals across Spain. Dozens are injured each year, mostly in falls.
In all, 15 people have died from gorings in Pamplona since record-keeping began in 1924 for the San Fermin festival.