The `Observable' position and other operators of particles of spins 0 and 1 (described by the Sakata-Taketani equations in Hamiltonian form) are investigated. It is shown that these are uniquely determined if it is required that the observable position must satisfy certain physically reasonable criteria, already applied by the authors to Dirac particles. The position operator coincides with that obtained by Case, who, however, assumed its form in a particular representation.