The Al-Cr system has been reviewed for Cr content up to 40 at.%. In this system several intermetallic compounds are formed by peritectic reactions. From the temperature of transformation and the composition of the phases, the nature of the invariant transformations is discussed. Transmission electron microscopy studies were performed on samples forming these compounds. A detailed structural interpretation is given for the phase theta-Al7Cr. A new structure is proposed for Al4Cr similar to that of the mu-Al4Mn phase of which the crystal structure is known. The phase Al5Cr (or Al11Cr2) was found to be orthorhombic and not monoclinic, as had been previously proposed. The existence of a cubic structure for the Al3Cr4 phase was confirmed. On account of previous results, we should point out that the phases theta-Al7Cr, Al4Cr and Al5Cr present characteristic features of pseudoicosahedral symmetry of the Al4Cr icosahedral phase: it has been verified in the case of theta and mu that the same type of atomic cluster may be considered in order to describe these structures, i.e. 12 atoms located at the vertices of deformed icosahedra (either 12Al or 11Al + 1Cr or 10Al + 2Cr) whose centres are occupied by a Cr atom. The reason for such an investigation originated from a study of the Al-Cr-Ni system for which the observed ternary structures appeared incoherent with those given for the binary Al-Cr system. This second study will be reported elsewhere.