In recent years the protection of structures from blasts has gained widespread attention with most of the effort on this subject focused on mitigating the local effects of the blast. With improved local protection, controlling the global response of structures subjected to impulsive types of loads is becoming increasingly important. In this paper, the passive mitigation of a structure's global response is examined through experimental blast tests of a large scale, 9-story structure equipped with a system of NESs. The system of NESs studied in this paper include two different types of devices, each of which employing a different type of restoring force; one type utilizes a smooth restoring force that is approximately cubic, while the other employs a linear restoring force coupled with one-sided vibroimpacts. The results of this study show that the passive NESs examined were capable of rapidly reducing the global response of the structure due to the blast loading. Additionally, the benefits of this passive system were demonstrated by its ability to reduce the peak demand on the structural system.