Weighted spaces of harmonic and holomorphic functions on the unit disc are discussed. It is shown that these spaces are always subspaces of c, , . Moreover, for many weights, it is shown that the weighted space of holomorphic functions has a basis. This paper is concerned with weighted spaces of harmonic and holomorphic functions on D = { z β¬6: IzI < l} (see section 2 for definitions). We show that these spaces are always subspaces of co. There are well known examples of weights such that the corresponding space Hvo(D) is not isomorphic to co, in fact it is not even a Zm-space ([3]). It turns out that weighted spaces of harmonic or holomorphic functions are 9,-spaces if and only it they are isomorphic to co (Corollary 2.4). The main problem we want to study is the question whether Hv,(D) has a basis. This will be answered positively for a large class of weights (Theorem 2.5). However, before we turn to weighted spaces, we prove, in section 1, an extension of a result of [6] about abstract BANACH spaces X. We investigate conditions on X such that X Oc, has a shrinking basis which are of independent interest. The results of section 1 then are applied to weighted spaces in section 2. 1. Let E, be a sequence of BANACH spaces. As usual we define (COE,)(o)={(e,):e,~E,, n = l , 2, ..., lim llenll =0} nm endowed with II(e,)ll =sup lle,Il, and Recall, a BANACH space Y has a shrinking basis (yk) if there are uniformly bounded projections P,: Y-, Y with P, 1 a k y k = 1 a k y k for all m ( 1 : ; ) k I 1