  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 afterglow's slow cooling phase.
