We report new results on the magnetic properties of the Fe x Co 1−x Ta 2 O 6 series of compounds. Essentially using neutron-diffraction and magnetic measurements we study, in more detail, the low-x limit of the temperature versus x phase diagram, where a new bicritical point is observed. The complete phase diagram shows three different magnetic phases at low temperature, for a high, intermediate and very low iron content. These phases consist of distinct antiferromagnetic orderings, characterized by different pairs of propagation vectors. We obtain information about the intraplane exchange interactions by fitting a high-temperature series of the magnetic susceptibility. Here we improve on a previously employed model, showing that two non-equivalent next-nearest-neighbor interactions must be taken into account in order to allow for in-plane magnetic orderings that are consistent with the neutron-diffraction results.