Math. Annalen 178, 131 144(1968) The Homotopy Category of Spectra. II DAN BURGHELEA and ARISTIDE DELEANU The present paper is the second part of a group of papers on the homotopy category of spectra. We define Cartan-Serre and Postnikov resolutions for spectra, as well as corresponding invariants. From this point of view this work is a parallel to the theory of Postnikov systems developed by A. Dold [9] for half exact functors. In the second part of the paper, by using these resolutions and some ideas of Shih Weishu as presented in the Cartan Seminar [7] we construct a spectral sequence for every generalized cohomology theory which is representable by a spectrum. This sequence is analogous to that of Atiyah and Hirzebruch, i.e. it relates the ordinary cohomology with coefficients in the groups of the point to the generalized cohomology. In fact, it seems probable that the two sequences are isomorphic. The advantage of the spectral sequence we present lies in the possibility of associating to every action of a group as group of automorphisms of a space of an action of the group on the spectral sequence. It is not clear how to do this for the Atiyah-Hirzebruch spectral sequence unless the group is a CW-complex acting cellularly on the space. This property of the sequence has been used [3] in the proof of some analogues for generalized cohomology theories of the theorem of Borel concerning the cohomology of the classifying spaces of compact Lie group. A drawback of this sequence consists in the fact that it is not clear how to define products on all of its terms. In the third part of the paper the Cartan-Serre resolutions are used in order to construct a spectral sequence which relates the homotopy of a spectrum to its homology, permitting in particular the analysis of the Hurewicz homo- morphism. This spectral sequence cannot be obtained for an arbitrary space since it works only in the stable range. The idea of this spectral sequence was suggested by the paper [1] of Adams 1. Some of the results in the present paper have been announced in [4] 2, [-5]. The authors are indebted to the referee for useful suggestions. § 0. Preliminaries The aim of this section is to recall some notations and results of D. Kan, G. W. Whitehead and of the authors. I After this paper was written, a paper of Donald Kahn appeared (Comm. Math. Helv. 40, 169 - 198 (1966)) in which he constructs an equivalent spectral sequence in the topological context. The last note in [4] contains some errors of indices, some of which are corrected in this paper. The last error appears in the Remark at the end of the note, which will be contained in a paper of the first named author. Added in Proof: This paper has now appeared [Inventiones Math. 5, 1--7 (1968)]. 10 Math, Ann, 178