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Untethered channel sounders are used to measure mobile radio propagation channels. As high data rate, millimeter-wave and multiple-input multiple output (MIMO) are considered in the next generation communications systems, knowledge of the propagation channel needs to be studied in high accuracy. Measuring time stability of the clocks in both transmitter and receiver is essential when characterizing relative delay between multipath components (MPCs), absolute delay, angle of arrival (AoA) and angle of departure (AoD) of MPCs. This paper describes timing circuit design of untethered electronic switched MIMO millimeter-wave channel sounders, proposes practical method to remove a constant initial time error, and experimentally estimates time stability of the channel sounders. Time stability is classified in three categories: short-term (in order of microseconds) that impacts relative delay, AoA and AoD; medium-term (in order of minutes) that impacts absolute delay; and long-term stability (in order of days) that can be calibrated. This is the first time to apply standard parameters for measuring clock stability, such as timing Allan deviation (TDEV) and time interval error (TIE), to channel sounding and modeling. Novel methods are developed for measuring jitter and short-term noise. It was found that TDEV for short-term measurements was less than 1 ps and the medium-term timing errors due to clock noise could be maintained at 0.4 ns/min.