We study a simple motion multiple capture pursuit differential game of m pursuers \(x_1, x_{2},..., x_{m}\) and one evader y. On the first k coordinates of the control function of each player a geometric constraint is imposed, and the other coordinates are subjected to an integral constraint. If \(x_{i_1}(\tau _1)=y(\tau _1),..., x_{i_d} (\tau _d)=y(\tau _d)\) for some pairwise distinct numbers \(i_1, i_{2},..., i_d \in \left\{ 1, 2,..., m\right\}\) and times \(0 < \tau _1 \le \tau _{2} \le ...\le \tau _d\) , then we say that d-multiple capture occurs. We obtain a sufficient condition for multiple capture to occur and construct strategies for the pursuers.
