Complexity of oilwell drillstrings makes unfeasible the direct application of control methodologies to suppress non-desired oscillations existing in these systems. A reasonable alternative is to develop operation recommendations and parameter selection methods to guide the driller to avoid such oscillations. In this paper, by using dynamical analysis tools, operation recommendations and the detection of safe drilling parameters in a conventional oilwell drillstring are presented. To this end, a more generic lumped-parameter model than those considered until now is proposed. Particularly, this model takes into account the fact that the drillstring length increases as drilling operation makes progress. The analysis of a sliding motion giving rise to self-excited bit stick-slip oscillations and bit sticking phenomena at the bottom-hole assembly is performed. Finally, the identification of key drilling parameters ranges for which non-desired torsional oscillations are present is carried out by studying Hopf bifurcations in the vicinity of the system equilibrium point when rotary velocities are greater than zero. © 2007 Elsevier Ltd. All rights reserved.