At Brannan Street, one car was hit by a SUV that police say was likely going too fast. The SUV ended up on the sidewalk.
Five people were transported to the hospital. It's unclear how severe their injuries were.
The other collision happened minutes earlier and just a few blocks away on Embarcadero at Harrison Street.
Police say the driver of a red Jaguar was trying to make an illegal left turn or U-turn when the car was broadsided by a Muni streetcar.
The three people in the Jaguar were taken to the hospital. Their injuries are not expected to be life threatening.
No one on the Muni streetcar was said to be injured. The streetcar has been taken out of service, which is standard procedure so workers can assess possible damage.
The accidents blocked off southbound lanes on the Embarcadero between Bryant and Brannan.