The complete sample of large-perihelion nearly-parabolic comets discovered during the period 1901-2010 is studied, starting with their orbit determination. Next, an orbital evolution that includes three perihelion passages (previous-observed-next) is investigated in which a full model of Galactic perturbations and perturbations from passing stars is 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. Using a series of simulations we show that this deep well is moderately resistant to some diffusion of the orbital elements of the analysed comets. It seems reasonable to assert 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 can appear only when their original semimajor axes are greater than 20000au. On the other hand, dynamically old comets are completely absent for semimajor axes longer than 40000au. We demonstrate that the observed 1/a_ori_-distribution exhibits a local minimum separating dynamically new from dynamically old comets. Long-term dynamical studies reveal a wide variety of orbital behaviour. Several interesting examples of the 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 the analysed comets.