The local dark matter is baryonic (low-mass stars or Jupiter-like objects), since non-baryonic matter is dissipationless and cannot form a highly flattened population.
The nature of the global dark matter has been a subject of discussion for long time. Initially it was suggested that in outer regions of galaxies low-mass dwarf stars dominate (Oort 1940, Ostriker et al. 1974, Roberts 1975). However, the stellar nature of galactic coronas/halos meets several difficulties. Coronas have larger dimensions than all known stellar populations, thus from hydrostatic equilibrium condition coronal stars must have much higher velocity dispersions than other populations. No fast-moving stars were found (Jaaniste & Saar 1975). If the hypothetical population is of stellar origin, it must be formed much earlier than all known populations, because known stellar populations of different age and metallicity form a continuous sequence of kinematical and physical properties, and there is no place where to include this new population (Einasto 1974). It is known that star formation is not an efficient process - usually in a contracting gas cloud only about 1 % of the mass is converted to stars. Thus we have a problem how to convert, in an early stage of the evolution of the Universe, a large fraction of the primordial gas into this population of dark stars.
The nature of dark matter was the basic problem discussed in the Caucasus Winter School and in the Dark Matter Conference in Tallinn (Doroshkevich et al. 1975). Silk (1974), Komberg & Novikov (1975) showed that gaseous coronas of galaxies and clusters cannot consist of neutral gas since the intergalactic hot gas would ionise the coronal gas. A corona consisting of hot ionised gas would be observable. A fraction of the coronal matter around galaxies and in groups and clusters of galaxies consists indeed of the X-ray emitting hot gas, but the amount of this gas is not sufficient to explain the flat rotation curves of galaxies (Turner 2003).
The baryonic nature (stars, gas) of the dark matter contradicts also the nucleosynthesis constraints mentioned already by Materne & Tammann (1976). A third very important observation was made which caused doubts to the baryonic matter as the dark matter candidate. The Cosmic Microwave Background radiation temperature and density fluctuations are much lower than the theoretically predicted limit 10-3 (see, for instance Parijskij 1978).
Then astronomers considered the possible existence of non-baryonic particles, such as heavy neutrinos. This suggestion was made independently by several astronomers (Szalay & Marx 1976 and others). If dark matter consists of heavy neutrinos, then this helps to explain the paradox of small temperature fluctuations of the cosmic microwave background radiation. Dark matter starts to condense at early epoch and forms potential wells, after the recombination baryonic matter flows into these wells and forms galaxies. However, numerical simulations of the formation of the structure of the neutrino-dominated dark matter Universe demonstrated, that in this case only supercluster-scale systems can form (see below).