In this paper nearly unstable AR(p) processes
(in other words, models with characteristic roots near the
unit circle) are studied. Our main aim is to describe the
asymptotic behavior of the least-squares estimators of the
coefficients. A convergence result is presented for the
general complex-valued case. The limit distribution is given
by the help of some continuous time AR processes. We apply
the results for real-valued nearly unstable AR(p)
models. In this case the limit distribution can be identified
with the maximum likelihood estimator of the coefficients of
the corresponding continuous time AR processes.