Flaxseed is abundant in cyclic peptides called linusorbs, which are derived from precursor proteins through post-translational modification. Previous studies have shown that four of the five precursor proteins contain repeat structures, where the variable linusorb domain is flanked by conserved signatures. The genome of flax cultivar CDC Bethune encodes 25 additional proteins which share the linusorbs-containing repeat pattern. Gene sequence analysis revealed that these repeats have arisen through three distinct modes of tandem duplication. Driven by the genetic diversity of potential linusorbs, here we continued to characterize these linusorb-related tandem repeats (LRTRs) at the amino acid level. Similar to known linusorbs, the linusorb-like domains (LLDs) are moderately hydrophobic in contrast to the hydrophilic spacers. The conserved flanking signatures of known linusorbs remain dominant among the LLDs, indicating a conserved role in the 30 proteins. Similarities of repeat pairs (RPs) across paralogous proteins are at the level between those within proteins and those across non-paralogues, suggesting the LRTRs in protein paralogues underwent adaptive evolution after ancestral gene duplication. Positive selection was identified to episodically act on certain sites and lineages of LRTRs both within and across paralogues. By combining all the evidence, we proposed a multi-dimensional model of adaptive evolution in cyclic peptide precursor proteins for the first time, which involves the concomitance of (a) protein paralogues divergence, (b) repeat divergence within protein paralogues and (c) repeat divergence across protein paralogues. Based on a single cultivated species, the proposed model serves as a prototype for broader evolutionary studies across other Linum species.