Ricci collineations of the Bianchi types I and III, and Kantowski–Sachs spacetimes are classified according to their Ricci collineation vector (RCV) field of the form (i)–(iv) one component of ξa(xb) is nonzero, (v)–(x) two components of ξa(xb) are nonzero, and (xi)–(xiv) three components of ξa(xb) are nonzero. Their relation with isometries of the spacetimes is established. In case (v), when det (Rab)=0, some metrics are found under the time transformation, in which some of these metrics are known, and the other ones new. Finally, the family of contracted Ricci collineations (CRC) are presented.