Asteroid 1999 AN 
will be again at 
from the Sun after
the beginning of June; by that time the uncertainty of its position on
the sky will grow to 
arc minutes (corresponding to
), that is any new observation will significantly contribute
to an improvement of the orbit. It is very likely that the
observations made in the second half of this year will allow to
determine the orbit well enough to predict accurately the 2027
encounter. This implies that some of the returns of the Table will be
discarded as incompatible with the observations; if the 2027 encounter
is not very deep, most of the close approaches in the Table would not
be possible any more.
The problem, however, will not go away, because all along the
variations line there are possible encounters occurring later, almost
every six months. E.g., we have analysed with our global
method the same 
multiple solutions discussed above over a
time span of 50 years after 2027, and found 165 possible returns, out
of which 117 in the moderate to low stretching region. This situation
is qualitatively stable: whatever the actual orbit is, it will not be
possible to predict with certainty the returns after the next close
approach for a time span longer than a few decades.
Since at least one node of 1999 AN will remain close to the
orbit of the Earth for centuries, this implies that this asteroid
shall have to be monitored, by observations and computations, for a
very long time. It is conceivable that at some time in the future a
decision could be made to deflect and/or destroy it. However, a
deflection decreasing the depth of some specific close approach could
increase the impact risk at a later date. Thus before such a decision
can even be contemplated we need to better understand the theory of
resonant and non-resonant returns, which has only been outlined in
this paper.