The canonical boundary-value problem for surface-plasmon-polariton (SPP) waves guided by the planar interface of a dielectric material and a plasmonic material was solved for cases wherein either partnering material could be a uniaxial material with optic axis lying in the interface plane. Numerical studies revealed that two different SPP waves, with different phase speeds, propagation lengths, and penetration depths, can propagate in a given direction in the interface plane; in contrast, the planar interface of isotropic partnering materials supports only one SPP wave for each propagation direction. Also, for a unique propagation direction in each quadrant of the interface plane, it was demonstrated that a new type of SPP wave -called a surface-plasmon-polariton-Voigt (SPP-V) wave -can exist. The fields of these SPP-V waves decay as the product of a linear and an exponential function of the distance from the interface in the anisotropic partnering material; in contrast, the fields of conventional SPP waves decay only exponentially with distance from the interface. Explicit analytic solutions of the dispersion relation for SPP-V waves exist and help establish constraints on the constitutive-parameter regimes for the partnering materials that support SPP-V-wave propagation. * E-mail: T.Mackay@ed.ac.uk. arXiv:1907.07211v2 [physics.optics] 4 Sep 2019 readily achieved indirectly via coupling with a prism [2][3][4] or surface-relief grating [5], for examples. SPP waves are of major technological importance: they have been widely exploited for optical sensing [5-7] and microscopy [8,9], and applications for optical communications [10][11][12][13][14] and harvesting solar energy [15][16][17] are on the horizon.The theory underpinning SPP-wave propagation is firmly established in the case where the two partnering materials are isotropic [1]. The case where an isotropic plasmonic material is partnered with an anisotropic dielectric material has also been considered previously [18][19][20]. However, SPP-wave propagation in the case where an anisotropic plasmonic material is partnered with an isotropic dielectric material has received scant attention from theorists, even though several experimental studies on this case have been reported recently [21][22][23][24][25][26].As we demonstrate in this paper, when anisotropic partnering materials are involved, some previously unreported SPP-wave characteristics emerge. Most notably, two different SPP waves, with different phase speeds, propagation lengths, and propagation depths, can propagate in a given direction in the interface plane. Analogously, this multiplicity of surface waves can also arise in the case of Dyakonov-wave propagation supported by dissipative anisotropic materials [27], and has also been reported in the case of SPP-wave propagation supported by periodically nonhomogeneous dielectric materials [28,29].Additionally, we demonstrate that when anisotropic partnering materials are involved, for a unique propagation direction in each quadrant of the interface plane...