A gas-kinetic traffic flow model is presented that describes the traffic flow operations of heterogeneous traffic on specific lanes of a motorway. To realistically portray the multilane dynamics of traffic flow, traffic is described as a collection of vehicle platoons that consist of an unconstrained vehicle followed by a nonnegative number of constrained followers. It is shown that the gas-kinetic dynamics of this unconstrained and constrained traffic are governed by continuum and noncontinuum processes. The continuum processes describe smooth changes in the mesoscopic traffic flow variables caused by motions in the phase space. The noncontinuum processes reflect, among other things, deceleration of vehicles due to interactions between vehicles from the same and from different user classes, immediate lane changing, postponed lane changing by constrained drivers, and spontaneous lane changing by free-flowing drivers. Finally, it is shown how the multilane-multiclass model relates to traditional aggregate-lane and mixed-class gas-kinetic equations. This is accomplished by aggregation across the motorway lanes and the user classes. It is shown that the expression reflecting vehicle interactions in traditional models is only valid for dilute traffic. A remedial expression is proposed.