GRB060505 and GRB060614 are nearby long-duration gamma-ray bursts (LGRBs) without accompanying supernovae (SNe) down to very strict limits. They thereby challenge the conventional LGRB-SN connection and naturally give rise to the question: are there other peculiar features in their afterglows which would help shed light on their progenitors? To answer this question, we combine new observational data with published data and investigate the multi-band temporal and spectral properties of the two afterglows. We find that both afterglows can be well interpreted within the framework of the jetted standard external shock wave model, and that the afterglow parameters for both bursts fall well within the range observed for other LGRBs. Hence, from the properties of the afterglows there is nothing to suggest that these bursts should have another progenitor than other LGRBs. Recently, Swift-discovered GRB080503 also has the spike + tail structure during its prompt gamma-ray emission seemingly similar to GRB060614. We analyse the prompt emission of this burst and find that this GRB is actually a hard-spike + hard-tail burst with a spectral lag of 0.8$pm$0.4 s during its tail emission. Thus, the properties of the prompt emission of GRB060614 and GRB080503 are clearly different, motivating further thinking of GRB classification. Finally we note that, whereas the progenitor of the two SN-less bursts remains uncertain, the core-collapse origin for the SN-less bursts would be quite certain if a wind-like environment can be observationally established, e.g, from an optical decay faster than the X-ray decay in the afterglows slow cooling phase.
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