Researchers in Spain recently conducted an experiment to evaluate the benefits of olive oil and walnuts. They compared the effects of consumption of these two health foods after participants ate a high fat meal. A commentary on yahoo news reported the following: "Both olive oil and walnuts decrease the onset of inflammation and oxidation in the arteries after a high-fat meal, but walnuts preserve the blood vessels' flexibility while olive oil does not, according to Ros. He attributed much of the beneficial effect to the alpha-linolenic acid found in walnuts. This nutrient is similar to the omega-3 fatty acids found in fish."
For more of an overview on healthy fats read my articles on cholesterol and on omegas.
Alpha-linolenic acid is an omega-3 fatty acid that provides many health benefits. It is, however, not a substitute for fish oil--only 2.7% of alpha-linolenic acid is converted to EPA and DHA. EPA and DHA are the vital omega-3's that most people are deficient in. For this reason I recommend fish oil in addition to food sources of alpha-linlenic acid such as walnuts and flax. I do not recommend high doses of flax oil since they are associated with an aggressive type of prostate cancer in men.
Link to the yahoo commentary.