In an image processing apparatus, a limit check procedure compares a capacity necessary for storing designated image files to be transferred and the residual memory capacity of a destination to which the image files should be transferred. The procedure determines whether or not the transfer of the image files is allowable on the basis of the result of comparison. This procedure is executed before and during the transfer of image files. The procedure executed before transfer obviates transfer failure when the image files are transferred to an external storage implemented by a CD-R or similar write limiting type of storing medium; in this case, the procedure is not necessary during transfer. In the event of transfer to a work memory built in the apparatus, even if transfer is allowed before transfer, the procedure is executed during transfer in order to produce an alarm when transfer becomes unallowable.