Welding task sequencing is a prerequisite in the offline programming of robot arc welding. Single-pass welding task sequencing can be modelled as a modified travelling salesman problem. Owing to the difficulty of the resulting arc-routing problems, effective local search heuristics are developed. Computational speed becomes important because robot arc welding is often part of an automated process-planning procedure. Generating a reasonable solution in an acceptable time is necessary for effective automated process planning. Several different heuristics are proposed for solving the welding task-sequencing problem considering both productivity and the potential for welding distortion. Constructive heuristics based on the nearest neighbour concept and tabu search heuristics are developed and enhanced using improvement procedures. The effectiveness of the heuristics developed is tested and verified on actual welded structure problems and random problems.