A laser cutting system for cutting a workpiece with a laser beam along a cutting line (L1, L2) at a variable cutting speed (v), comprising a movable machining head for placing the laser beam on the respective workpiece, comprising a user interface for specifying the respective cutting line (L1, L2) and for specifying a minimum path accuracy (ΔB) of the laser beam, comprising a control device for controlling a movement of the machining head along the cutting line (L1, L2) relative to the respective workpiece and for controlling a plurality of process variables (LL, Tp, ΔT, DF, D0, ModL, δB, DS, DD, AG, PG) of a cutting process, wherein with said movement during the cutting process a cutting path (B1, B2) of the laser beam along the cutting line (L1, L2) can be created, wherein a first subset of the process variables comprises exclusively one or a plurality of process variables (LL, Tp, ΔT), which influence the power of the laser beam available for cutting, and wherein a second subset of the process variables comprises exclusively one or a plurality of process variables (DF, D0, ModL, δB, DS, DD, AG, PG), which have no influence on the power of the laser beam available for cutting, wherein the control device a) is embodied such that the movement of the machining head can be controlled by the control device during the cutting process such that the cutting path (B1, B2) of the laser beam follows the cutting line (L1, L2) within the minimum path accuracy (ΔB), wherein a kinematic state of the machining head can be changed by increasing or reducing the speed (v) of the machining head relative to the workpiece b) comprises registering means for registering a change of the kinematic state of the machining head and/or at least of a value of the speed (v) of the machining head and/or of a value for a change of the speed of the machining head, c) at least one process variable of the first subset (LL, Tp, ΔT) can be changed by means of the control device in response to or after a change of the kinematic state of the machining head depending on at least one of the respectively registered values (vg1, vg2) for the speed of the machining head and/or of at least one of the respectively registered values for a change of the speed (δv1, δy2, δv3) of the machining head, characterized in that at least one process variable of the second subset (DF, D0, ModL, δB, DS, DD, AG, PG) can be changed by means of the control device in response to or after a change of the kinematic state of the machining head depending on the speed (v) of the machining head, wherein the change of the respective process variable can be controlled depending on at least one variable control parameter (S20, S21, S22, S23, S24, S25, S26, S27), the respective value of which can be determined by the control device based on rules implemented in the control device depending on at least one of the respectively registered values (vg1, vg2) of the speed of the machining head and/or of at least one of the respectively registered values for a change (δv1, δy2, δv3) of the speed of the machining head. a) is embodied such that the movement of the machining head can be controlled by the control device during the cutting process such that the cutting path (B1, B2) of the laser beam follows the cutting line (L1, L2) within the minimum path accuracy (ΔB), wherein a kinematic state of the machining head can be changed by increasing or reducing the speed (v) of the machining head relative to the workpiece b) comprises registering means for registering a change of the kinematic state of the machining head and/or at least of a value of the speed (v) of the machining head and/or of a value for a change of the speed of the machining head, c) at least one process variable of the first subset (LL, Tp, ΔT) can be changed by means of the control device in response to or after a change of the kinematic state of the machining head depending on at least one of the respectively registered values (vg1, vg2) for the speed of the machining head and/or of at least one of the respectively registered values for a change of the speed (δv1, δy2, δv3) of the machining head, characterized in that