The invention relates to a method and a device for sequencing nucleic acid mols. on a perforated membrane. The inventive method and device can be esp. used in multiplex sequencing. The method involves prepg. an oligonucleotide that is labeled to satn. with base-specific fluorescent dyes that is then immobilized on a filter. The labeled sequence is then processively degraded with an exonuclease with the released bases being detected fluorometrically. [on SciFinder (R)]