An engine air intake system for an engine-powered working machine includes a lever cover which covers at least a base portion of an operation control lever mounted on an operation handle for operation by a human operator to control operation of at least one of the working machine and an engine of the working machine, a lower cover disposed inside the lever cover so as to define jointly with the lever cover a hollow space, an air intake portion having an air inlet opening and disposed in the lever cover such that at least the air inlet opening is disposed within the hollow space, and a fresh air guide hose interconnecting the air intake portion and the interior of an air-cleaner case.