The paper investigates the coagulation-fragmentation equations \[ C_j(t) = {1 \over 2} \sum^{j - 1}_{k = 1} W_{j - k,k} \bigl( C(t) \bigr) - \sum^\infty_{k = 1} W_{j,k} \bigl( C(t)\bigr), \quad j = 1,2,3, \dots, \] where \(W_{j,k} (C(t)) = a_{j,k} \cdot C_j(t) C_k(t) - b_{j,k} \cdot C_{j + k} (t)\). The author proves the existence and uniqueness of admissible solutions for coagulation coefficients \(a_{j,k}\) satisfying \(a_{j,k} \leq K_\alpha \cdot (j \cdot k)^\alpha\) with \(\alpha \in ({1 \over 2}, 1]\), and for fragmentation coefficients satisfying a strong fragmentation condition.