The pair interaction energy of charged colloidal particles in electrolyte solutions can exhibit a large barrier as well as a pronounced secondary minimum. We discuss the effect of a secondary energy minimum on aggregation kinetics by modeling irreversible dimer formation as a two-step process in which charged colloidal particles in electrolyte solutions first aggregate reversibly into the secondary minimum before they can cross the energy barrier. In the classical regime of slow aggregation, the secondary minimum is seen to have a pronounced effect if either the ionic strength of the solution is high (e.g., 0.1 M for particles of 150-nm radius) or particles are large (greater than or equal to 350-nm radius for an ionic strength of 0.01 M). Under these conditions, our calculations predict a transient period of fast aggregation into the secondary minimum followed by slow primary aggregation. The aggregation in this second regime is found to take place at a lower rate than what would be expected in the absence of the secondary minimum or from an earlier linearized model for secondary aggregation. The crossover time between the two regimes strongly depends on the particle size but not on the particle concentration, which however determines the degree of aggregation reached within the fast regime. We also conclude that a previously observed severe discrepancy between measured and predicted aggregation rate constants for submicron particles is nor due to the neglect of secondary aggregation in the theoretical treatment.