A time clock modem transmitter comprises a pseudo-random number generator (PNG) which produces a time-spaced sequence of pseudo-random numbers such that each number uniquely represents the time of day. A transmitter PNG(11) capable of producing a polynomial sequence longer than 24 hours is reset every 24 hours by a transmitter reference clock (4). A receiver clock modem includes a receiver PNG(26) having the same polynomial characteristics as the transmitter PNG(11). A received signal number is fed into the receiver PNG and the PNG is then started. The output from the receiver PNG and the received signal are then compared to ensure correct synchronization of the receiver clock modem. A detector is provided which is responsive to the random number representing 2400 hours such that it produces a resetting output pulse at 2400 hours to reset a receiver reference clock. Clock pulse generators 19 and 28 are provided to rapidly advance by one cycle on actuation the reference clock and PNG respectively in the transmitter and the receiver for resetting the clocks.