This article argues that the forms in -ontas, labeled participles or gerunds in the literature are in reality verbal adverbs or converbs. This hypothesis is tested on the basis of the cross- linguistic criteria proposed in Ηaspelmath & Κönig (eds., 1995). Special emphasis is placed on finiteness, which creates problems for these forms if defined in terms of agreement and tense/aspect specification. Ιt is shown that the forms are specified for both aspect and relative tense, but it is argued that this does not prevent them from being non-finite; on a scale of finiteness they would in fact be placed at a rather low point both within Greek and cross-linguisticalΙy and this not only allows them to be categorized as converbs, given that they meet aΙl the other criteria, but places them among the prototypical exponents of the category.