Small encrusting marine organisms belonging to the genera Ascodictyon, Eliasopora and Vinella were originally described as ctenostome bryozoans. Well-preserved ascodictyid specimens from the Early and Middle Devonian of Poland allow us to exclude such an affinity due to the absence of any aperture in the ascodictyid vesicles for the protrusion or withdrawal of the lophophore during feeding. The ctenostome bryozoans are soft-bodied, but the ascodictyid vesicles and filaments have calcified walls. Reinterpretation of Eliasopora stellata (Nicholson & Etheridge, 1877), Eliasopora sparsiforme (Kiepura, 1965) and ‘Ascodictyon’ venustum Kiepura, 1965, provides a basis for the recognition of a new group of extinct Palaeozoic organisms, defined by a combination of morphological features including the presence of a thread-like network of perforate branching filaments, perforate vesicles formed by swollen tips of the filaments, and the ability of filaments to fuse. This distinguishes Ascodictyidae from all other known extant microorganisms. The shape, size and perforated walls of vesicles make ascodictyids similar to the Palaeozoic tuberitinid ‘foraminifers’. It remains to be determined which morphology is plesiomorphic and which is derived.