A protein's chemical properties, the chain conformation, the function of the protein and its species specificity are determined by the information contained in the amino acid sequence. Proteins of similar functions have at some level sequential identical amino acid sequences. The closer the phylogenetic relationship, the more similar are the sequences. To find the similarities between two or more protein sequences is of great importance for protein sequence analysis. The differences in the amino acid sequences permit the construction of a family tree of evolution. In this work, a comparison method was devised that is capable of analysing a protein sequence 'hierarchically', i.e. it can examine a protein sequence at different spatial resolutions. Based on a wavelet decomposition of protein sequences and a cross-correlation study, a sequence-scale similarity concept is proposed for generating a similarity vector, which renders the comparison of two sequences feasible at different spatial resolutions (scales). This new similarity concept is an expansion of the conventional sequence similarity, which only takes into account the local pairwise amino acid match and ignores the information contained in coarser spatial resolutions.