The stability of dipositronium is discussed. Our purpose is not to compete with highly accurate calculations that are available but point out that its dissociation energy can be understood on the basis of simplified models if satisfying the important requirement of consistency in the description of the 'atoms' and molecules of positronium. The importance of correlations in positronium and dipositronium is analyzed. Also studied is the replacement of positrons by heavier Fermions in positronium and dipositronium. It is found that the Born-Oppenheimer approximation is valid provided the mass of the heavier Fermions exceeds 200 times the mass of the electron. (C) 2014 Elsevier B.V. All rights reserved.