Trial-and-error procedure for implementation of system optimum (SO) congestion pricing with unknown demand functions are built upon two underlying assumptions: the demand function is time-invariant during the implementation period and the travelers are informed and immediately adjust to the user equilibrium (UE) after updating link tolls.These two assumptions are relaxed and new trial-and-error procedures are developed in this paper by considering a time-varying demand function and flow evolution process towards the UE.Three cases are investigated.When the demand is time-varying but user equilibrium is reached during an intra-trial interval, triggered by the variance of the demand, an adaptive trial-and-error procedure is developed and the bound of time-varying SO link flow is established.When the demand is time-invariant but link flow follows an evolution process,the relationship is discerned among the adjustingrateof travelers to theUE link flow and the trial interval.For the general case with time-varying demand and flow evolution process, a new trial-and-error procedure is proposed to deal withthe time variance of demand and the evolution of link flow.These scenarios and procedures are demonstrated with numerical examples.