Creating a dictionary out of the lines in second file would be a faster solution and it will get rid of the duplicates too:
from collections import defaultdict
second_file = open('second.txt')
second_file_dict = defaultdict(int)
first_file_dict = defaultdict(int)
for line in second_file:
second_file_dict[line.strip()] += 1
second_file.close()
first_file = open('first.txt')
for line in first_file:
if line in second_file_dict and not in first_file_dict:
print line
first_file_dict[line.strip()] += 1
first_file.close()
