A new mathematical formulation for scheduling multipurpose continuous processes is presented. The formulation is based on the state-task network representation, coupled with an event-driven representation of time, resulting in a mixed-integer linear programming model. Event points are defined by the end of task execution for all continuous tasks in the process. Timing constraints are applied to continuous tasks involving the same material state to ensure feasibility of rate-based material balances. The formulation allows for unit-dependent variable processing rates, sequence-dependent changeovers, and dedicated and flexible intermediate storage requirements. Several variants of a medium to large scale continuous manufacturing process are examined to illustrate the applicability and efficiency of the method. The formulation is shown to compare favorably with existing continuous-time models; a new optimal solution on the finite intermediate storage case of the process is also established.