1. Membrane-bound nucleus: Eukaryotic cells are defined by the presence of a nucleus, a membrane-bound organelle that houses the cell's genetic material (DNA).

2. Membrane-bound organelles: In addition to the nucleus, eukaryotic cells have other membrane-bound organelles, such as mitochondria, Golgi apparatus, endoplasmic reticulum, lysosomes, etc. These organelles perform specialized functions within the cell.

These two characteristics distinguish eukaryotes from prokaryotes, which lack a nucleus and other membrane-bound organelles.