Are the works of Saul Bellow considered Existentialist?
Existentialism is defined by a focus on despair, angst, the significance -- or lack thereof -- of the small human in the large world, the unreality of the mind vs. matter, the line between real and unreal, and the concrete vs. the abstract, especially as it pertains to absurdism (Wikipedia). In literature, Franz Kafka and Phillip K. Dick both wrote in the Existentialist style.
Saul Bellow's books have been labeled Existentialist, especially his most famous book, Herzog, but Bellow was, at heart, an optimist, and so his works generally did not have the deep despair of true Existentialism. Herzog in particular is Existentialist only in its format; it is styled as a series of letters, written in the mind by the main character, who faces his demons with this "unreal" method instead of in reality. When he is shocked out of his inner turmoil by a very real arrest, he is able to come to terms with his own issues. The story is not tragic or meaningless enough to be termed truly Existentialist, and Bellow's other books are similar; Henderson the Rain King is a comedic farce, and although the main character is somewhat Existentialist in his thinking, he too learns to accept himself and matures by the end.