 In the 18th century, the Spanish believed that the Mbayá numbered seven to eight thousand people.When first in contact with Spanish explorers in the early decades of the 16th century, the Mbayá lived north of the Pilcomayo River on the western side of the Paraguay River.In 1542, the Spanish Governor of Paraguay Álvar Núñez Cabeza de Vaca with Guarani allies launched a large military operation against the Mbayá northeast of Asunción.