Neural networks and reinforcement learning have successfully been applied to various games, such as Ms. Pacman and Go. We combine multilayer perceptrons and a class of reinforcement learning algorithms known as actor-critic to learn to play the arcade classic Donkey Kong. Two neural networks are used in this study: the actor and the critic. The actor learns to select the best action given the game state; the critic tries to learn the value of being in a certain state. First, a base game-playing performance is obtained by learning from demonstration, where data is obtained from human players. After this off-line training phase we further improve the base performance using feedback from the critic. The critic gives feedback by comparing the value of the state before and after taking the action. Results show that an agent pre-trained on demonstration data is able to achieve a good baseline performance. Applying actor-critic methods, however, does usually not improve performance, in many cases even decreases it. Possible reasons include the game not fully being Markovian and other issues.