The paper proposes two estimation approaches for duration models that are subject to right censored observations and selection effects. Main focus is on accelerated duration models and the estimators that are of the limited information type, i.e. they are not based on a fully specified selection model. The estimators are instrumental variable adaptations to the Powell symmetrically trimmed least squares and the Buckley-James estimators for right censored data. In a small Monte Carlo study they are found to perform well. Empirical results are presented for total time outside the unemployment state for participants in the Swedish Adult Education Initiative and labour market training. The latter ones are included as controls and are found to have significantly longer times outside the unemployment state. There are strong indications of selection effects.