A hydraulic work machine, comprising: a first hydraulic pump and a second hydraulic pump of variable displacement type; a left track device including a left track hydraulic motor driven by hydraulic fluid supplied from the first hydraulic pump; a right track device including a right track hydraulic motor driven by hydraulic fluid supplied from the second hydraulic pump; a hydraulic actuator (33, 34, 35) driven by hydraulic fluid supplied from at least one of the first hydraulic pump and the second hydraulic pump; a work implement driven by the hydraulic actuator (33, 34, 35); a travel operation device (6, 7) for operating the left track device and the right track device; and a work operation device (8, 9) for operating the work implement,; a controller that controls pump displacements of the first hydraulic pump and the second hydraulic pump in response to an operation of the travel operation device (6, 7); characterized in that the hydraulic work machine further comprises: a travel operation detector configured to detect operation contents of the travel operation device (6, 7); a work operation detector configured to detect operation contents of the work operation device (8, 9); a first pressure detector configured to detect a first pump pressure that is a delivery pressure of the first hydraulic pump; and a second pressure detector configured to detect a second pump pressure that is a delivery pressure of the second hydraulic pump, the controller is configured to calculate, when the controller decides from detection results of the travel operation detector and the work operation detector that the work implement is not operated but the travel operation device (6, 7) is operated and besides the left track device and the right track device are straightly traveling, an anomaly decision evaluation value based on a value obtained by subtracting one from other of the first pump pressure and the second pump pressure and to decide based on a result of comparison between the anomaly decision evaluation value and a predetermined decision reference value that one of the left track device and the right track device has an anomaly. a first hydraulic pump and a second hydraulic pump of variable displacement type; a left track device including a left track hydraulic motor driven by hydraulic fluid supplied from the first hydraulic pump; a right track device including a right track hydraulic motor driven by hydraulic fluid supplied from the second hydraulic pump; a hydraulic actuator (33, 34, 35) driven by hydraulic fluid supplied from at least one of the first hydraulic pump and the second hydraulic pump; a work implement driven by the hydraulic actuator (33, 34, 35); a travel operation device (6, 7) for operating the left track device and the right track device; and a work operation device (8, 9) for operating the work implement,; a controller that controls pump displacements of the first hydraulic pump and the second hydraulic pump in response to an operation of the travel operation device (6, 7); characterized in that the hydraulic work machine further comprises: a travel operation detector configured to detect operation contents of the travel operation device (6, 7); a work operation detector configured to detect operation contents of the work operation device (8, 9); a first pressure detector configured to detect a first pump pressure that is a delivery pressure of the first hydraulic pump; and a second pressure detector configured to detect a second pump pressure that is a delivery pressure of the second hydraulic pump, the controller is configured to calculate, when the controller decides from detection results of the travel operation detector and the work operation detector that the work implement is not operated but the travel operation device (6, 7) is operated and besides the left track device and the right track device are straightly traveling, an anomaly decision evaluation value based on a value obtained by subtracting one from other of the first pump pressure and the second pump pressure and to decide based on a result of comparison between the anomaly decision evaluation value and a predetermined decision reference value that one of the left track device and the right track device has an anomaly. a travel operation detector configured to detect operation contents of the travel operation device (6, 7); a work operation detector configured to detect operation contents of the work operation device (8, 9); a first pressure detector configured to detect a first pump pressure that is a delivery pressure of the first hydraulic pump; and a second pressure detector configured to detect a second pump pressure that is a delivery pressure of the second hydraulic pump, the controller is configured to calculate, when the controller decides from detection results of the travel operation detector and the work operation detector that the work implement is not operated but the travel operation device (6, 7) is operated and besides the left track device and the right track device are straightly traveling, an anomaly decision evaluation value based on a value obtained by subtracting one from other of the first pump pressure and the second pump pressure and to decide based on a result of comparison between the anomaly decision evaluation value and a predetermined decision reference value that one of the left track device and the right track device has an anomaly.