Both attacks happened early Tuesday morning -- one near 51st Street and Avenue N 1/2 and the other along the Seawall near 45th Street.
The attack on the Seawall happened in the early morning daylight. The victim tells us the worst part for her was after her attacker took off, nobody stopped to help her.
"In that one-second glance, I could see his shadow coming and it was just one swift motion, He grabs me and I was down on the ground," the victim said.
The attack lasted less than five minutes. But the victim, a Galveston resident who didn't want to be identified, says she was in the fight for her life.
"The first thing that came to my mind was reach for his eyes, where can you put a person down at besides there," she said.
According to Galveston police, the attacks happened about 30 minutes apart Monday morning. The first attack was at 5:50am in the 4700 block of the Seawall. The second happened not far down the road at 51st and Avenue N 1/2.
"A Hispanic male matching the same description attacked her from behind, but she carried a metal pipe with her when she ran and she was able to hit him and he took off running," Galveston Police Department Lt. Michael Gray said.
The women who spoke with us Tuesday afternoon says while she was fighting the man, he attempted to pull off her shorts. She says luckily, when she ripped his shirt in the fight, he jumped back in his car and drove off.
"I didn't know what else to do but fight. I didn't know what else to do," the victim said.
She wants to send a message to all women not to give up if you ever find yourself in the same situation.
"Don't back down defend yourself, stand your ground. Maybe that's what scared him off is me putting up a good fight," she said.
Police are currently investigating both of these attacks.
The attacker got away in a white Mitsubishi Galant with LED lights in the side-view mirror.
If you have information that can help police find this man, call Galveston Police at 409-765-3702.