The main features of the low-latitude Neoproterozoic glaciations remain the subject of controversial debates concerning possible triggers. Here we use an AGCM coupled with a slab ocean to test one of the earliest and simplest explanation for tropical glaciations: a higher obliquity of the Earth's rotation axis. We show that high obliquity may result in an extensive glaciation during the Sturtian episode (750 Ma), due to the location of continental masses in the tropical areas, but cannot produce a large glaciation in the case of mid to high latitude paleogeographies such as those thought to typify the Varangian-Vendian episodes (620--580 Ma).