In a medium mixing bowl combine cucumber slices and sweet pepper strips. Set aside.
For vinaigrette, in a screw-top jar combine walnut oil or salad oil, water, red wine vinegar, basil, salt, pepper, and dash ground red pepper. Cover and shake well. Pour vinaigrette over cucumber mixture. Toss lightly to coat. Cover and refrigerate for 4 to 24 hours.
Before serving, stir in walnuts. Makes 4 to 6 servings.