Can unstable relics save pure Cold Dark Matter?

The standard CDM model fails to describe the power spectrum of fluctuations since it gives too much power at small scales. Among other possible improv ements, it has barn suggested that an agreement with observations can be ac hieved with the addition of a late decaying particle, through the injection of nonthermal radiation and the consequent increase of the horizon length at the equivalence time. We analyze the possibility of implementing this id ea in some extensions of the electroweak standard model, discussing the cos mological and astrophysical bounds to which these schemes are subject. (C) 2000 Elsevier Science B.V. All rights reserved. PACS: 12.60.Jv: 14.60.St; 9 5.35. + d; 98.65. - r; 98.80.Cq.