Three- and two-photon excitation of high-lying energy levels of ${\mathrm{Nd}}^{3+}$ was realized in La${\mathrm{F}}_{3}$: ${\mathrm{Nd}}^{3+}$ crystals using fundamental radiation of a tunable ${\mathrm{Ti}}^{3+}$ -sapphire laser. Strong UV and green-red luminescence lines were obtained by the three- and two-photon excitation process, respectively. The UV luminescence due to the three-photon excitation was observed to be delayed by about 25 ns from the visible luminescence due to the two-photon excitation. A mechanism of the excitation and luminescence process is proposed.