In a large saucepan, cook mushrooms, celery, onion, and pepper in cooking oil until vegetables are tender.
Stir in wild rice and cook 1 minute more. Add chicken stock or broth, marjoram, tarragon, and thyme. Bring to boiling; reduce heat. Cover and simmer for 15 minutes.
Add long-grain rice; simmer for 25 to 30 minutes more or until rice is tender and liquid is absorbed. Let stand, covered, for 5 minutes before serving. Makes 6 to 8 side-dish servings.