We present an investigation of line-of-sight (LOS) velocity oscillations in solar faculae and sunspots. To study the phase relations between chromospheric and photospheric oscillations of the LOS velocity, we measured the time lag of the chromospheric signal relative to the photospheric one for several faculae and sunspots in a set of spectral line pairs. The measured time lags are different for different objects. The mean measured delay between the oscillations in the five-minute band in faculae is 50 s for the Si i 10 827 Å – He i 10 830 Å pair; for the pair Fe i 6569 Å – Hα 6563 Å the mean delay is 20 s; for the pair Fe i 4551 Å – Ba ii 4554 Å the mean delay is 7 s; for the pair Si i 8536 Å – Ca ii 8542 Å the mean delay is 20 s. For the oscillations in the three-minute band in sunspot umbrae the mean delay is 55 s for the Si i 10 827 Å – He i 10 830 Å pair; for the Fe i 6569 Å – Hα 6563 Å pair it was not possible to determine the delay; for the Fe i 4551 Å – Ba ii 4554 Å pair the mean delay is 6 s; for the Si i 8536 Å – Ca ii 8542 Å pair the mean delay is 21 s. Measured delays correspond to the wave propagation speed, which significantly exceeds the generally adopted speed of sound in the photosphere. This raises the question of the origin of these oscillations. The possibility that we deal with slow MHD waves is not ruled out.