In an electron beam apparatus comprising an enclosure in which an electron-emitting device having an electron-emitting region between opposite electrodes is disposed, the electron-emitting device exhibits such a characteristic as that an emission current is uniquely determined with respect to a device voltage. The interior of the enclosure is maintained under an atmosphere effective to prevent structural changes of the electron-emitting device. An image-forming apparatus comprises an enclosure in which an electron source and an image-forming member are disposed, the electron source comprising the above electron-emitting device. An emission current is stable with a very small change in the amount of electrons emitted, a sharp image is produced with high contrast, and gradation control is easily carried out.