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Transmetalation is the stoichiometric replacement of the metals in a polymetallic target T with different metals from reagents called transmetalators, TM. Transmetalation at useful rates under mild conditions is an excellent source of large families of discrete heteropolymetallic complexes. Direct transmetalation gives heteropolymetallic products containing the same number of metal atoms as T. Replacement of just one metal center in T with a different metal from TM is called monotransmetalation. Replacement of a particular metal in a heteropolymetallic target T with another metal from TM is specific. Preferred reaction of T with one of a mixture of TM and TM' is selective. This paper discusses the kinetics and mechanisms of real and model monotransmetalations of neutral T with neutral TM in aprotic solvents. Transmetalation requires the breaking and making of many different bonds, but most monotransmetalation systems exhibit just one kinetic event whose rates and rate laws vary with T and TM. The observed event can be formation of reaction precursors P or P1, metal exchange within P or P1, rearrangement of successor complexes S or S' or their dissociation to separate products. The concentrations and proportions [P]/[F] and [S]/[S'] depend on the reactants and the experimental temperature. Overall rates and transmetalation selectivity depend on TM stabilities. Transmetalation specificity results from correlated thermodynamic factors in P/F assembly and kinetic factors in activated complex formation. The most common slow transmetalation step is metal exchange.