Organic upconversion devices (OUCs) consist of an organic infrared photodetector and an organic visible light-emitting diode (OLED), connected in series. OUCs convert photons from the infrared to the visible and are of use in applications such as process control or imaging. Many applications require a fast OUC response speed, namely the ability to accurately detect in the visible a rapidly changing infrared signal. Here, high image-contrast, narrowband OUCs are reported that convert near-infrared (NIR) light at 980 and 976 nm with a full-width at half maximum of 130 nm into visible light. Transient photocurrent measurements show that the response speed decreases when lowering the NIR light intensity. This is contrary to conventional organic photodetectors that show the opposite speed-versus-light trend. It is further found that the response speed increases (when using a phosphorescent OLED) or decreases (for a fluorescent OLED) when increasing the driving voltage. To understand these surprising results, an analysis by numerical simulation is conducted. Results show that the response speed behavior is primarily determined by the electron mobility in the OLED. It is proposed that the low electron drift velocity in the emitter layer sets a fundamental limit to the response speed of OUCs.