Nonvanishing derived limits in shape theory

For compact Hausdorff spaces X the nth derived limit of the mth homology progroup vanishes, for all n ⩾ 2 and m ⩾ 1. The main purpose of this paper is to show that, in contradistinction to the compact case, for any choice of integers n,m ⩾ 1, there exists a paracompact space, X, whose nth derived limit of the mth homology progroup (integer coefficients) does not vanish.