The present paper generalises results by Tadaki [12] and Calude et al. [1] on oscillation-free partially random infinite strings. Moreover, it shows that oscillation-free partial Chaitin randomness can be separated from oscillation-free partial strong Martin-Lof randomness by       $\Pi_{1}^{0}$    -definable sets of infinite strings.
['Ludwig Staiger']
On oscillation-free chaitin h-random sequences