Marvel’s Spider-Man season two premiere date announced While the titular web-slinger can still be seen in theaters in Infinity War, fans can look forward to seeing the animated version of Marvel’s Spider-Man return to the small screen for its second season on Disney XD, which will premiere on Monday, June 18. The second season of Marvel’s Spider-Man follows Peter Parker in his sophomore year as a more experienced Super Hero and a more confident student at what was once the intimidating Horizon High School.