A vital role in supporting successful functioning of biological cells is played by membrane channels called antiporters. These channel proteins utilize the concentration gradient of one type of species to move another type of species in the opposite direction and against their concentration gradient. It is believed that antiporters operate via alternating conformational transitions that expose these proteins to different sides of the membrane, and that only thermodynamics controls the activation of these channels. Here we explicitly investigate a chemical-kinetic model of antiporters to argue that there are additional kinetic constraints that need to be satisfied for these channels to be operational. This implies that kinetics and not thermodynamics governs the functioning of antiporters. In addition, the efficiency of antiporters is analyzed and the most optimal operating conditions are discussed. Our theoretical analysis clarifies some important aspects of the molecular mechanisms of biological membrane transport.