Using a food processor fitted with the grating attachment, shred the carrots and celery root to achieve slaw-like, julienned pieces.
Combine the carrots, celery, onions, mayonnaise, vinegar, caraway and sugar in a large non-reactive bowl. Mix well until fully incorporated, and then season with salt and pepper. Chill in refrigerator until cold, 1 hour.
Will keep in the fridge for 5 days, stored in an airtight container.