The main goal of the presentation is to show how a newly developed method of complete bifurcation groups (MBG) and concepts of rare attractors (RA) helps to find unknown dangerous regimes in machine dynamics [1-4]. The paper considers scenarios of appearance of rare dangerous attractors [in typical dissipative oscillation systems with one degree of freedom, nonlinear elastic characteristics of hard type and harmonic excitation. Two types of elastic symmetric nonlinear suspension are examined: with trilinear symmetric and asymmetric characteristics and with a cubic characteristic of Duffing’s type. The bifurcations diagrams with rare attractors and their domains of attraction are plotted using NLO [5] and SPRING [6] software. For trilinear systems the exact analytical solutions of rare attractors and the exact monodromy matrixes for stability evaluation have found as well. Basins of attraction have built and their comparison also has done for two systems with different parameters. It is shown that rare attractors may be dangerous. Two bifurcation diagrams have been compared: the one have built using the usual ‘brute-force method’ which allows to do parameter continuation only along the stable branches [8] , and the second bifurcation diagram, with rare attractors, have build using our method of complete bifurcation groups [7]. Our conclusion: using the complete bifurcation analysis it is possible to find parameter regions, in the typical dynamical systems with nonlinear suspension, with the unexpected dangerous regimes (rare attractors) and to prepare necessary parameters or state conditions. The same approaches may be useful for other tasks of nonlinear machine dynamics, such as active control of vibrations, impact- and vibro-technology, dynamics of smart elastic-damping materials.