Definably compact groups definable in real closed fields

We study definably compact definably connected groups definable in a sufficiently saturated real closed field R. Our main result is that for such a kind of groups G that are also abelian, there is a Zariski-connected R-algebraic group H such that the o-minimal universal covering group of G is, up to a locally definable isomorphism, an open connected locally definable subgroup W of the o-minimal universal covering group of H(R)₀. Thus, G is definably isomorphic to the definable quotient of W by a discrete subgroup.