In a covered saucepan cook potatoes in boiling water for 20-25 minutes or till just tender; drain well. Peel and cube potatoes.
In a very large bowl whisk together mayonnaise or salad dressing, vinegar, mustard, salt and pepper. Add celery, green pepper and onion. Add potatoes and eggs. Toss lightly to mix. Cover and chill for 6 to 24 hours.