We show that it is impossible to determine the time a tunneling particle sp
ends under the barrier. However, it is possible to determine the asymptotic
time, i.e., the time the particle spends in a large area including the bar
rier. We propose a model of time measurements. The model provides a procedu
re for calculation of the asymptotic tunneling and reflection times. The mo
del also demonstrates the impossibility of the determination of the time th
e tunneling particle spends under the barrier. Examples for delta form and
rectangular barrier illustrate the obtained results.