It should be noted that d(a t 2 +a 2 2 )/dt and dSl/dt both behave like {a^a^) 2 as one approaches the point of bifurcation. 7 The singularity which this expression manifests at £2 2 = 4B n (where dynamical instability sets in) is spurious: Eq. (15), without the substitution (16), leads to the result a= £2±(0.4Z?£2 5 )Results of a phase-shift analysis with and without the use of a Regge-pole model in K + p elastic scattering from 0.86 to 1.95 GeV/c are described. We have obtained four possible solutions, all of which indicate resonantlike behavior in one partial-wave amplitude. Three of our solutions yield a P 3 / 2 partial wave with a behavior consistent with the Breit-Wigner resonance formula. The properties of such a Z* resonance are described.We have reported earlier a preliminary phaseshift analysis of K + p elastic-scattering data from 0.86 to 1.95 GeV/c. 1 Since then an extensive random search for solutions has been carried out. The data used in the analysis include new polarization measurements 2 at 1.89 GeV/c which we obtained using a butanol-alcohol target 3 at 26 kG. These new measurements are in good agreement with the old ones which were taken with a lanthanum-magnesium-nitrate target. We have also included recent polarization data at 0.86 and 0.96 GeV/c by Andersson et al. 1 We have obtained four possible solutions, all of which indicate res-onantlike behavior in one partial-wave amplitude. The same results were obtained when analysis was repeated using predictions for high partial waves from a Regge-pole model.In our energy-independent analysis, we have found typically about 50 solutions (XV^DF^ 2.5) at each momentum. By examining all the partial waves simultaneously, we noted that these solutions clustered into several areas on Argand diagrams. To select the best of these, we first required that each group vary with increasing momentum on the Argand diagram in a smooth, continuous way in each partial wave; this test elimi- Table I. Outline of phase-shift solutions.