We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation,while the catalyst aggregates of the same species B or C perform self-coagulation processes.By means of the generalized Smoluchowski rate equation based on the mean-field assumption,we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel K(i,j;l) ∝ l ν and the catalysis-fragmentation rate kernel F(i,j;l) ∝ l μ,where l is the size of the catalyst aggregate,and ν and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate.The relation between the values of parameters ν and μ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A.It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters ν and μ,but also depend on the values of these two parameters.When ν > μ and ν≥ 0,the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution a k(t) obeys the conventional or generalized scaling law;when ν < μ and ν≥ 0 or ν < 0 but μ≥ 0,the catalysis-fragmentation process may play a dominating role and a k(t) approaches the scale-free form;and in other cases,a balance is established between the two competing processes at large times and a k(t) obeys a modified scaling law. We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation processes. By means of the generalized Smoluchowski rate equation based on the mean-field assumption, we study the kinetic behaviors of the system with the catalysis-coagulation rate kernel K (i, j; l) α lν and the catalysis-fragmentation rate kernel F (i, j; where l is the size of the catalyst aggregate, and ν and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate.The relation between the values ​​of parameters ν and μbly the competing roles between the two catalysis processes in the kinetic evolution of species A. It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviors are not determined simply by the relation between the t wo parameters ν and μ, but also depend on the values ​​of these two parameters.When ν> μ and ν≥0, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution ak (t) obeys the conventional or generalized scaling law; when ν <μ and ν ≥ 0 or ν <0 but μ ≧ 0, the catalysis-fragmentation process may play a dominating role and ak (t) approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ak (t) obeys a modified scaling law.