The primary taxa of eukaryote classification should be monophyletic and based on fundamental cell structure rather than nutritional adaptive zones. The classical two kingdom classification into "plants" and "animals" and the newer four kingdom classifications into "protis", "fungi" "animals" and "plants" are therefore both unsatisfactory. Eukaryotes can be classified into nine kingdoms each defined in terms of a unique constellation of cell structures. Five kingdoms have plate-like mitochondrial cristae: (1) Eufungi (the non-ciliated fungi, which unlike the other eight kingdoms have unstacked Golgi cisternae), (2) Ciliofungi (the posteriorly ciliated fungi), (3) Animalia (Animals, sponges, mesozoa, and choanociliates; phagotrophs with basically posterior ciliation), (4) Biliphyta (Non-phagotrophic, phycobilisome-containing, algae; i.e. theGlaucophyceae and Rhodophyceae), (5) Viridiplantae (Non-phagotrophic green plants, with starch-containing plastids). Kingdom (6), the Euglenozoa, has disc-shaped cristae and an intraciliary dense rod and may be phagotrophic and/or phototrophic with plastids with three-membraned envelopes. Kingdom (7), the cryptophyta, has flattened tubular cristae, tubular mastigonemes on both cilia,m and starch in thecompartment between the plastid endoplasmic reticulum and the plastid envelope; their plastids, if present, have phycobilins inside the paired thylakoids and chlorophyll c2. Kingdom (8), the Chromophyta, has tubular cristae, together with tubular mastigonemes on one anterior cilum and/or a plastid endoplasmic reticulum and chlorophyll c1 + c2. Members of the ninth kingdom, the Protozoa, are mainly phagotrophic, and have tubular or vesicular cristae (or lack mitochondria altogether), and lack tubular mastigonemes on their (primitively anterior) cilia; plastids if present have three-envelop membranes, chlorophyll c2, and no internal starch, and a plastid endoplasmic reticulum is absent. Kingdoms 4-9 are primitively anteriorly biciliate. Detailed definitions of the new kingdoms and lists of the phyla comprising them are given. Advantages of the new system and its main phylogenetic implications are discussed. A simpler system of five kingdoms suitable for very elementary teaching is possible by grouping the photosynthetic and fungal kindoms in pairs. Various compromises are possible between the nine and five kingdoms systems; it is suggested that the best one for general scientific use is a system of seven kingdoms in which the Eufungi and Ciliofungi become subkingdoms of the Kingdom Fungi, and the Cryptophyta andChromophyta subkingdoms of th Kingdom Chromista; the Fungi, Viridiplantae, Biliphyta, and Chromista can be subject to the Botanical Code of Nomenclature, while the Zoological Code can govern the Kingdoms Animalia, Protozoa and Euglenozoa...