Graduation involves several steps. You have to

1. complete all your courses, that is, obtain an absolutorium,
2. submit a thesis title by the given deadline,
3. satisfy all language requirements,
4. register for the final examination in Neptun (even if you are retaking it),
5. register the main topic and subsidiary topic of your final examination (only BA students)
6. prepare and submit a thesis
7. and pass the final examination.

BA

http://seaswiki.elte.hu/studies/BA/major/graduation

MA American

http://seaswiki.elte.hu/studies/MA/American/Graduation

MA English

http://seaswiki.elte.hu/studies/MA/English/graduation