[en] Large amplitude, turbulent Alfvénic fluctuations have been commonly observed in the solar wind since the first in situ measurements. An important but still unexplained property of such nonlinear fluctuations seen typically in the fastest streams is that, despite the large excursion of the magnetic field fluctuations, the magnitude of the total magnetic field remains nearly constant, a condition that corresponds to spherical polarization. How is this Alfvénic turbulent state achieved in the solar wind remains a fundamental open question in space physics. Although nonlinear Alfvénic fluctuations have been studied for several decades, most of previous work has considered a plasma in thermodynamic equilibrium. The solar wind however displays many non-thermal features and here we discuss how non-thermal effects, in particular pressure anisotropy, and nonlinearities affect the stability and nonlinear evolution of Alfvénic fluctuations with constant total magnetic field magnitude in different plasma-β regimes. (paper)