Context :

Aims : KIC 8975515 is a Kepler double-lined spectroscopic binary system with hybrid pulsations .
Two components have similar atmospheric properties ( T _ { eff } \sim 7400 K ) , and one of them is a fast rotator ( v \sin i = 162 versus 32 km/s ) .
Our aim is to study the Kepler light curve in great detail in order to determine the frequencies of the pulsations , to search for regular spacing patterns in the Fourier spectrum , if any , and to discuss their origin in the context of binarity and fast rotation .

Methods : In this paper , we study the properties of the stellar pulsations based on a careful analysis in the low- , intermediate- and high-frequency regions of the Fourier spectrum .
This is done by performing repeated frequency-search analyses with successive prewhitenings of all the significant frequencies detected in the spectrum .
Moreover , we searched for regular period spacings among the g modes , as well as frequency splitting among the g and p modes .

Results : In the low-frequency regime , five regular period spacing patterns including one series of prograde g modes and four series of retrograde r modes were detected .
The r modes are well-distributed with respect to the harmonics of the rotational frequency of the fast-rotating star f _ { rot } = 1.647 d ^ { -1 } .
The dominant g mode is f _ { 2 } = 2.37 d ^ { -1 } .
The strongest p mode , at f _ { 1 } = 13.97 d ^ { -1 } , forms a singlet .
In the high-frequency region , we identified two multiplets of regularly split p modes with mean frequency spacings of 0.42 d ^ { -1 } and 1.65 d ^ { -1 } .

Conclusions : We detected some series of retrograde r and prograde g modes as well as two multiplets of p modes with frequency spacings related to the stellar rotation of both components of the twin system KIC 8975515 .
We identified the fast-rotating component as a hybrid pulsator with r modes and the slowly-rotating component as a \delta Sct pulsator .