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Metastable rare gas atoms are gaining increasing interest for their potential in the development of optically pumped laser systems. Understanding the time evolution of excited rare gas states in a collisional environment is of importance for the possibility of exploiting them as the active laser species. Collisional deactivation rates for excited states of Kr$\mathrm{<mrow\; data-mjx-texclass="ORD">\ast </mrow>}$($4p5$$5p1$) atoms colliding with ground state Kr ($4p6$) and He ($1s2$) have been measured by time resolved measurements of the laser induced fluorescence, following state selective excitation at room temperature. Collisional energy transfer for the Kr$\mathrm{<mrow\; data-mjx-texclass="ORD">\ast </mrow>}$($4p5$$5p1$) + Kr ($4p6$) and Kr$\mathrm{<mrow\; data-mjx-texclass="ORD">\ast </mrow>}$($4p5$$5p1$) + He ($1s2$) systems were investigated in a pulsed electrical discharge. Metastable Kr$\mathrm{<mrow\; data-mjx-texclass="ORD">\ast </mrow>}$($4p5$$5s1$) was generated by electron impact excitation from the ground state. Using a pulsed tunable dye laser these metastable states were pumped to selected upper levels of the 2$p$ manifold (Paschen notation) and time-dependent fluorescence decay data from pumped and collisionally populated levels were collected. The total and intramultiplet state-to-state collisional deactivation rate constants were derived from the experimental data and by numerical models. The experimental data were simulated by fitting to numerical solutions of a set of coupled differential equations describing the full collisional relaxation processes. State-to-state rate constants are reported.