Eukaryotic Exceptions. Most eukaryotic cells -- those that contain nuclei -- also contain mitochondria, but there are exceptions to this rule. Some parasitic protists, for example, take energy from their hosts and do not have mitochondria, as explained by an article in the Journal of Eukaryotic Microbiology. In humans, mature red blood cells, or erythrocytes, lack mitochondria as well, as reported by the Encyclopedia Britannica.