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Because surface plasmon polaritons (SPPs) are surface waves characterized by one free transverse dimension, the only monochromatic diffraction-free spatial profiles for SPPs are cosine and Airy waves. Pulsed SPP wave packets have been recently formulated that are propagation-invariant and localized in the in-plane dimensions by virtue of a tight spectral association between their spatial and temporal frequencies, which have thus been dubbed `space-time' (ST) SPPs. Because of the spatio-temporal spectral structure unique to ST-SPPs, the optimal launching strategy of such novel plasmonic field configurations remains an open question. We present here a critical step towards realizing ST-SPPs by reporting observations of ultrabroadband striped ST-SPPs. These are SPPs in which each wavelength travels at a prescribed angle with respect to the propagation axis to produce a periodic (striped) transverse spatial profile that is diffraction-free. We start with a free-space ST wave packet that is coupled to a ST-SPP at a gold-dielectric interface, and unambiguously identify the ST-SPP via an axial beating detected in two-photon fluorescence produced by the superposition of incident ST wave packet and the excited surface-bound ST-SPP. These results highlight a viable approach for efficient and reliable coupling to ST-SPPs, and thus represent the first crucial step towards realization of the full potential of ST-SPPs for plasmonic sensing and imaging.