@katrielalex's solution is more pythonic, but if you did need to modify the list in-place without making a copy, you could use a while loop and break when you catch an IndexError.
e.g.
nums = [1,1,1,2,2,3,3,3,5,5,1,1,1]
def remove_adjacent(nums):
"""Removes adjacent items by modifying "nums" in-place. Returns None!"""
i = 0
while True:
try:
if nums[i] == nums[i+1]:
# Letting you figure this part out,
# as it's a homework question
except IndexError:
break
print nums
remove_adjacent(nums)
print nums
Edit: pastebin of one way to do it here, in case you get stuck and want to know..