This paper presents 28 GHz and 73 GHz millimeter-wave propagation measurements performed in a typical office environment using a 400 Megachip-per-second broadband sliding correlator channel sounder and highly directional steerable 15 dBi (30° beamwidth) and 20 dBi (15° beamwidth) horn antennas. Power delay profiles were acquired for 48 transmitter-receiver location combinations over distances ranging from 3.9 m to 45.9 m with maximum transmit powers of 24 dBm and 12.3 dBm at 28 GHz and 73 GHz, respectively. Directional and omnidirectional path loss models and RMS delay spread statistics are presented for line-of-sight and non-line-of-sight environments for both co- and cross-polarized antenna configurations. The LOS omnidirectional path loss exponents were 1.1 and 1.3 at 28 GHz and 73 GHz, and 2.7 and 3.2 in NLOS at 28 GHz and 73 GHz, respectively, for vertically-polarized antennas. The mean directional RMS delay spreads were 18.4 ns and 13.3 ns, with maximum values of 193 ns and 288 ns at 28 GHz and 73 GHz, respectively.