Timing parameters are presented for 59, mostly southern, pulsars derived from observations using the Molonglo Observatory Synthesis Telescope over about 2.4 yr from 1986 to 1988. For 45 of the pulsars, either the positions or the period parameters are more accurate than those previously available. Comparisons of the new and previously published parameters show good agreement in most cases. However, several apparently significant position changes are obtained and, in six cases at least, these can be interpreted as proper motions. Significant changes in period parameters are also observed in several pulsars, and evidence is found for one or more large glitches in the period of PSR 1641 - 45.