According to The Virtual Fossil Museum, secondary endosymbiosis is the process that occurs when the product of primary endosymbiosis is taken up and retained by a eukaryote. Primary endosymbiosis is the engulfment of a bacterium by an organism. Secondary endosymbiosis gives rise to different forms of algae.
"Secondary Endosymbiosis" by J.M. Archibald explains how endosymbiosis led to the development of several forms of alga. A heterotrophic eukaryote engulfed an ancestor of cyanobacteria. This ancestor of cyanobacteria became a permanent part of its cell as an organelle in the cytoplasm. This primary endosymbiosis gave rise to the differentiation of red algae, glaucophyte algae and green algae with double-membrane plastids. Secondary endosymbiosis occurred when another eukaryote engulfed and retained the alga containing the primary plastids.
With secondary endosymbiosis, three or four membranes may surround secondary plastids, according to The Virtual Fossil Museum. The two additional membranes are said to correspond to the membrane of the host cell and the alga that was engulfed.
When one organism lives inside another, the process is called endosymbiosis, according to the Genetics Science Learning Center from University of Utah. Mitochondria and chloroplasts are two structures that may have become permanent fixtures in the cell through endosymbiosis. They have similar features to bacterial cells, including separate DNA from the nucleus of the cell. This, along with the fact they both have double membranes, suggests they were ingested by another host.