Before we can answer, it would be helpful to know you chromatographic conditions. What solvents, modifiers, and column? How was it loaded- what was it dissolved in?
Double peaks can come a number of ways. Depending on the pKa of groups on the peptide, and the pH of the mobile phase, one can see double peaks. Dissolving the sample in a solvent that is too strong can also cause split peaks. Or, as mentioned above, it could be something with the molecule, too.
A key could be to evaluate the multiple possibilities regarding 3D conformation of your peptide structure. Try to heat your HPLC column during the analytic run. Best wishes.
with all the information provided, its hard to conclude what they are. They could possibly be epimers which will obviously show identical mass. The possibility of having a different conformer is there as well. Why don't you check the proton mmr of this peptide? Also I can suggest to run analytical RP-HPLC at various temperatures and check if the ratios between the peak areas change (thus, suggesting conformational inhomogeneity), if you have a column heater equipped with your HPLC instrument. Do you have proline (s) by any chance?
Definitely! Happened to me twice: the peptides were "impossible to purify", because two conformations were in an equilibrium. The interconversion rate was slow (hours).