The attacks Monday morning left many women on guard.
"I was actually going to go running this morning by myself because I travel a lot and don't mind getting out and running, but when I heard that, I thought no, too dangerous," Galveston visitor Betty Troyer said.
"I think it's crazy. I mean, I run here all the time and everyone seems so nice," seawall jogger Kayleigh Pope said.
And they're thinking about ways to protect themselves.
"I carry a Taser. I have a Taser usually on me all the time," Galveston visitor Sharon Holley said.
Galveston police say the first attack happened around 5:45am as a woman jogged while listening to music. Police have identified the attacker as 24-year-old Christopher Adrian Vela.
Vela is accused of trying to pull the jogger's shorts down but she scratched him in the face before he ran away. Less than 30 minutes later, investigators believe Vela attacked another woman who escaped after striking him with a pipe.
"Yes, one of the victims did fight and do some of the recommended actions to prevent an attack -- scratch, bite, kick, scream and was able to actually assault the suspect back, so we may be able to use that as evidence in identifications," Galveston Police Chief Henry Porretto said.
The chief says they developed a person of interest pretty quickly at the scene and found Vela at his home near the scene of the attacks. Then he says further forensics and identification by the victims allowed them to go back and make an arrest Wednesday.
That brings relief to a lot of women.
"Thanks goodness he's not out there anymore," Pope said.
"Feel safer, a little safer," Troyer said.
But it's also a reminder of what can happen any time.
"Even though there's a lot of people out here, a lot of people walking up and down the beach and running, still you just never know," Holley said.
Vela is now facing two charges of attempted sexual assault. His bond has been set at $500,000. Police say he's also a possible suspect in an unrelated sexual assault case.