We investigate line formation processes in Type IIb supernovae ( SNe ) from 100 to 500 days post-explosion using spectral synthesis calculations . The modelling identifies the nuclear burning layers and physical mechanisms that produce the major emission lines , and the diagnostic potential of these . We compare the model calculations with data on the three best observed Type IIb SNe to-date - SN 1993J , SN 2008ax , and SN 2011dh . Oxygen nucleosynthesis depends sensitively on the main-sequence mass of the star and modelling of the [ O I ] \lambda \lambda 6300 , 6364 lines constrains the progenitors of these three SNe to the M _ { ZAMS } = 12 - 16 M _ { \odot } range ( ejected oxygen masses 0.3 - 0.9 M _ { \odot } ) , with SN 2011dh towards the lower end and SN 1993J towards the upper end of the range . The high ejecta masses from M _ { ZAMS } \gtrsim 17 M _ { \odot } progenitors give rise to brighter nebular phase emission lines than observed . Nucleosynthesis analysis thus supports a scenario of low-to-moderate mass progenitors for Type IIb SNe , and by implication an origin in binary systems . We demonstrate how oxygen and magnesium recombination lines may be combined to diagnose the magnesium mass in the SN ejecta . For SN 2011dh , a magnesium mass of 0.02 - 0.14 M _ { \odot } is derived , which gives a Mg/O production ratio consistent with the solar value . Nitrogen left in the He envelope from CNO burning gives strong [ N II ] \lambda \lambda 6548 , 6583 emission lines that dominate over H \alpha emission in our models . The hydrogen envelopes of Type IIb SNe are too small and dilute to produce any noticeable H \alpha emission or absorption after \sim 150 days , and nebular phase emission seen around 6550 Å is in many cases likely caused by [ N II ] \lambda \lambda 6548 , 6583 . Finally , the influence of radiative transport on the emergent line profiles is investigated . Significant line blocking in the metal core remains for several hundred days , which affects the emergent spectrum . These radiative transfer effects lead to early-time blueshifts of the emission line peaks , which gradually disappear as the optical depths decrease with time . The modelled evolution of this effect matches the observed evolution in SN 2011dh .