beta type phases, formed by a diffusive process during cooling ZrO2-2xN4x/3 down below 1000 degrees C, have been investigated structurally by XRD and TEM methods. They show trigonally distorted fluorite structures with anion vacancies ordered along the unique axis. The individual beta type phases (beta, beta’, beta ") can be described by arrangements of Bevan clusters (Zr7O8N4) and Zr7O14 units stacked along this direction. For the oxygen rich beta’ phase, prepared by quenching the high temperature phase in water, an average sequence of one Bevan cluster and one Zr7O14 unit is detected. An average modulation length corresponding to c(beta n)=4.1c(beta) is observed in the case of the beta " phase. The basic building unit to form the structure of the beta phase is only the Bevan cluster.