We present a class of efficient algorithms for global combine operations in k-port message-passing systems. In the k-port communication model, in each communication round, a processor can send data to k other processors and simultaneously receive data from k other processors. We consider algorithms for global combine operations in n processors with respect to a commutative and associative reduction function. Initially, each processor holds a vector of m data items and finally the result of the reduction function over the n vectors of data items, which is also a vector of m data items, is known to all n processors. We present three efficient algorithms that employ various trade-offs between the number of communication rounds and the number of data items transferred in sequence. For the case m=1, we have an algorithm which is optimal in both the number of communication rounds and the number of data items transferred in sequence.