This paper addresses a problem of natural language text alignment, from a humanities discipline called textual genetic criticism where different text versions must be compared. The paper shows that this task is hard because such versions can be very different and texts with a lot of internal repetitions present specific difficulties. MEDITE is a natural language text aligner that compares texts written in the same language. It detects modifications at character level, as opposed to related applications which either remain at word level or give poor results at character level. The detection of moved blocks in the text, induced by our formalism based on edit distance with moves, is introduced. The algorithm is closely related to sequence alignment in bioinformatics as similar building blocks are used and applied to this natural language processing task. A benchmark analysis has been carried out to compare MEDITE with other aligners and it shows that our approach is superior to existing ones especially in hard cases.