  The complete sample of large-perihelion nearly-parabolic comets discovered
during the period 1901-2010 is studied starting from their orbit determination.
Next, an orbital evolution that includes three perihelion passages
(previous-observed-next) is investigated where a full model of Galactic
perturbations and perturbations from passing stars have been incorporated. We
show that the distribution of planetary perturbations suffered by actual
large-perihelion comets during their passage through the Solar system has a
deep, unexpected minimum around zero which indicates a lack of "almost
unperturbed" comets. By a series of simulations we show that this deep well is
moderately resistant to some diffusion of orbital elements of analysed comets.
It seems reasonable to state that the observed stream of these large-perihelion
comets experienced a series of specific planetary configurations when passing
through the planetary zone. An analysis of the past dynamics of these comets
clearly shows that dynamically new comets may appear only when their original
semimajor axes are greater than 20 000 au. However, only for semimajor axes
longer than 40 000 au dynamically old comets are completely not present. We
demonstrated that the observed $1/a_{\rm ori}$ distribution exhibits a local
minimum separating dynamically new from dynamically old comets. Long-term
dynamical studies reveal a large variety of orbital behaviour. Several
interesting examples of action of passing stars are also described, in
particular the impact of Gliese 710 which will pass close to the Sun in the
future. However, none of the obtained stellar perturbations is sufficient to
change the dynamical status of analysed comets.
