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Experimental results on the phase slip process in superconducting leadnanowires are presented under two different experimental conditions: constantapplied current or constant voltage. Based on these experiments we establisheda simple model which gives us the condition of the appearance of phase slipcenters in a quasi-one-dimensional wire. It turns out that the competitionbetween two relaxations times (relaxation time of the absolute value of theorder parameter $\tau_{|\psi|}$ and relaxation time of the phase of the orderparameter in the phase slip center $\tau_{\phi}$) governs the phase slipprocess. Phase slip phenomena, as periodic oscillations in time of the orderparameter, is possible only if the gradient of the phase grows faster than thevalue of the order parameter in the phase slip center, or equivalently if$\tau_{\phi}<\tau_{|\psi|}$.Comment: 13 pages, 15 figure

Condition for the occurrence of phase slip centers in superconducting nanowires under applied current or voltage