We have measured the excited state absorption in $Ce:YAlO_{3}$, crystals for the first time and assigned it for a 5d$ ightarrow$conduction band transition. Two broad absorption bands were observed at 555 nm and 465 nm fowllowing the 308 nm XeCl laser excitation and their cross sections and oscillator strengths were calculated. We have also measured the fluorescence lifetimes in between 300 K and 700 K to study the nonradiative relaxation from the lowest 5d state of $Ce^{3+}$ ions and explained ESA and the transition process from the state in terms of a configurational coordinate.dinate.