The two natural hazards caused by the movement of plates under the Earth's surface are:

1. Earthquakes: These occur when tectonic plates shift, causing the ground to shake violently. The movement can be either sudden or gradual, but the resulting energy release can be devastating.

2. Volcanoes: When plates collide, one plate can slide under the other (subduction). The descending plate melts, and the molten rock rises to the surface, creating volcanoes. Volcanic eruptions can release ash, lava, and gases, which can be hazardous to life and property.