We consider dipolar anisotropies in the universal expansion triggered by bulk peculiar flows. Starting with the deceleration parameter, we employ the familiar expansion tensor and introduce a new direction-dependent parameter, namely the deceleration tensor. Using linear cosmological perturbation theory we identify an apparent (Doppler-like) dipolar anisotropy in the sky distribution of the deceleration parameter, which is due to the observer’s peculiar motion and it is closely analogous to the dipole seen in the Cosmic Microwave Background. In practice, this means that the bulk-flow observers should “see” their universe accelerating faster towards a certain point on the celestial sphere and equally slower towards the antipodal. Typically, the dipole axis should lie fairly close to that of the microwave background, though the two dipoles should not necessarily coincide. Also, given that peculiar velocities fade away on progressively larger scales, the magnitude of the dipolar anisotropy in the deceleration parameter should decrease with increasing redshift. Finally, we show that peculiar motions leave an apparent dipolar imprint in the sky distribution of the Hubble parameter as well.