A cell image processing apparatus comprising: an imaging unit for imaging a specimen smeared on a slide glass, and obtaining a cell image of a cell included in the smeared specimen; a display; and a processing unit being configured to perform operations comprising: obtaining a plurality of characteristic values based on a plurality of cell images obtained by the imaging unit, each of the plurality of characteristic values respectively representing a predetermined characteristic of each of the plurality of cell images; and controlling the display so as to display a screen showing a temporal fluctuation in the obtained characteristic values, the cell image processing apparatus further comprising a staining unit for staining the cell included in the specimen smeared on the slide glass, wherein the processing unit obtains a first characteristic value representing a state of a staining unit, said first characteristic value relating to a brightness value of a color component of pixels in a nucleus area in the cell image, and obtains a second characteristic value representing a state of the imaging unit, said second characteristic value relating to a brightness value of a color component of pixels in a background area in the cell image. an imaging unit for imaging a specimen smeared on a slide glass, and obtaining a cell image of a cell included in the smeared specimen; a display; and a processing unit being configured to perform operations comprising: obtaining a plurality of characteristic values based on a plurality of cell images obtained by the imaging unit, each of the plurality of characteristic values respectively representing a predetermined characteristic of each of the plurality of cell images; and controlling the display so as to display a screen showing a temporal fluctuation in the obtained characteristic values, the cell image processing apparatus further comprising a staining unit for staining the cell included in the specimen smeared on the slide glass, wherein the processing unit obtains a first characteristic value representing a state of a staining unit, said first characteristic value relating to a brightness value of a color component of pixels in a nucleus area in the cell image, and obtains a second characteristic value representing a state of the imaging unit, said second characteristic value relating to a brightness value of a color component of pixels in a background area in the cell image. obtaining a plurality of characteristic values based on a plurality of cell images obtained by the imaging unit, each of the plurality of characteristic values respectively representing a predetermined characteristic of each of the plurality of cell images; and controlling the display so as to display a screen showing a temporal fluctuation in the obtained characteristic values, the cell image processing apparatus further comprising a staining unit for staining the cell included in the specimen smeared on the slide glass, wherein the processing unit obtains a first characteristic value representing a state of a staining unit, said first characteristic value relating to a brightness value of a color component of pixels in a nucleus area in the cell image, and obtains a second characteristic value representing a state of the imaging unit, said second characteristic value relating to a brightness value of a color component of pixels in a background area in the cell image.