A system, method and computer program product for steering a time-of-day (TOD) clock for a computer system having a physical clock providing a time base for executing operations that is stepped to a common oscillator. The method includes receiving, at a processing unit, a request to change a clock steering rate used to control a TOD-clock offset value for the processing unit, the TOD-clock offset defined as a function of a start time (s), a base offset (b), and a steering rate (r). The unit schedules a next episode start time with which to update the TOD-clock offset value. After updating TOD-clock offset value (d) at the scheduled time, TOD-clock offset value is added to a physical-clock value (Tr) value to obtain a logical TOD-clock value (Tb), where the logical TOD-clock value is adjustable without adjusting a stepping rate of the oscillator.