The diversity of peptide libraries synthesized according to the ＇＇mixing and portioning＇＇ concept producing libraries containing one peptide per bead is limited by the number of beads. A method for the generation and screening of peptide libraries with increased molecular diversity by synthesis of many peptides on each of the beads is described. According to this approach, in each synthesis cycle, every portion of the beads gets a mixture of amino acids, thus the total number of peptides is larger then the number of beads in the library. The degree of heterogeneity is increases from the N- to the C-terminal. Positions close to the N-terminal include relatively few amino acids, whereas positions closer to the C-terminal include a higher number of amino acids. This structure allows generation of extensive diversity on each bead, while still retaining the ability to identify the peptide by N-terminal sequencing. The identification of the peptides on selected beads is achieved by sequencing and by using a self-encoding system. This self-encoding system allows the use of coded as well as non-coded amino acids which cannot be identified by automatic sequencers. According to this system, each non-coded amino acid is presented in a mixture with a coded amino acid. The coded amino acid serves as an indicator for the presence of the non-coded one. Only a portion of the target sequence is identified by N-terminal sequencing. Once partial sequence information is obtained, secondary libraries are synthesized in order to find out which amino acids present in each position are responsible for binding a ligand. The new approach enables generation and screening of up to about 10(15) peptides per library, increasing the diversity of solid phase-screened peptides, or other non-sequenceable polymer libraries, by up to 10(7)-fold, thereby increasing the chances of discovering structures of interest.