The process of asexual reproduction
In desmids, asexual reproduction takes place by simple cell division. In the first instance it is the nucleus, situated in the centre of the isthmus, that multiplies (a process which is hardly or not to be observed light microscopically as it requires fixation and staining with specific dyes).
Following this process, between the daughter nuclei a new cell wall, as a transverse septum in the lengthened isthmus, is constituted. Subsequently, the istmial compartments separated by this septum gradually grow to new semicells. The mutual contact between the two developing, young semicells is maintained for a long time so that cell division results in formation of a couple of daughter cells which initially, by way of their young semicells, are still linked to each other.