Branched oligopeptides prepared by coupling a very hydrophobic aspartic diamino acid ethyl ester such as Asp $(LeuEt)_2$, $Asp(IleEt)_2$ and $Asp(PheEt)_2$ to glycine or glycylphenylalanine were grafted to the cyclotriphosphazene backbone bearing an equimolar hydrophilic poly(ethylene glycol) (PEG). The properties of the resultant amphiphiles were examined in comparison with those of the linear oligopeptide analogues previously reported. All cyclic phosphazene trimers grafted with the branched tetra- and pentapeptides displayed a normal trend of thermosensitivity depending on their hydrophilic to hydrophobic balance, but the stability and particle size of their micelles were found to be greatly dependent on the fine structure of the branched oligopeptides grafted. The trimers bearing branched tetrapeptides with a low hydrophobicity were found to form unstable micelles initially, which reassemble into thermodynamically more stable polymersomes.