This is the second edition of the Catalogue of the Components of Double and Multiple stars (CCDM). The first one, of which a detailed description has been given in Communication de l'Observatoire Royal de Belgique, Serie A, 115, 1994, may be found at the CDS under reference <I/211>. The complete description of this second edition is published (in French and English) in "Observations et Travaux", a review edited by the Societe Astronomique de France. A detailed historical sketch of the creation and development of the catalogue -- which served as double star data base for the preparation of the HIpparcos Input Catalogue <I/196> -- has been published in issue 25, pp.29-31 (1999) of this same review. There are no fundamental differences between the two editions: format, presentation and construction are similar. The main difference lies in the important increase of the considered systems of which number expands from 34.031 to 49.325. Few additions exist in the description of the contents of the various columns, and some new codes had to be used for references to astronomical positions, especially related to the introduction of new Hipparcos systems or components to known systems (see the "refpos.dat" file). Concerning the names of the systems in columns 16 to 22, one has also to mention some additions to those given in the INDEX-WDS (C.E.Worley, 1984). They are: AOT = Oss. di Torino ACG = Astr.Cat.Greenw. BAC = P.Bacchus BEW = U.Bastian et al. CRI = F.Crifo DUF = M.Duflot DYL = J. Doyle HDS = Hipparcos JRN = A. Jorissen JKS = M.P.Jenniskens KZA = S.M.Kazeza LMP = P.Lampens LYS = L. Louys MCO = McCormick NYS = O.Nys ONL = Occult. News Letters PWS = Th.Pauwels RSU = M.Rousseau SLE = G.Soulie VHS = P.Verhas Note that: MAL = McAlister in WDS 1984 MCA = McAlister in WDS 1994 Some changes have finally been brought to the names of particular STT and STF systems (App) as shown here, to avoid some confusion that exists with the non (App) systems: --> For STF (App)I, addition of 4000, i.e. STF 4001 instead of STF 1(App)I STF 4002 instead of STF 2(App)I ............... STF 4060 instead of STF 60(App)I --> For STF (App)II, addition of 5000, i.e. STF 5003 instead of STF 3(App)II ............... STF 5012 instead of STF 12(App)II --> For STT (App)I, addition of 4000, i.e. STT 4001 instead of STT 1(App) STT 4005 instead of STT 5(App) ............... STT 4256 instead of STT 256(App)