Organisms composed of unstructured cells surrounded by membranes are called prokaryotes.

Here's why:

* Unstructured cells: Prokaryotic cells lack a nucleus and other membrane-bound organelles that are characteristic of eukaryotic cells. Their DNA is located in a region called the nucleoid, but it's not enclosed within a membrane.

* Surrounded by membranes: Prokaryotic cells are enclosed by a plasma membrane, which regulates the passage of substances into and out of the cell.

Examples of prokaryotes include bacteria and archaea.