  We generalise the concept of radially self-accelerating beams, to the domain
of optical pulses. In particular, we show, how radially self-accelerating
optical pulses (RSAPs) can be constructed by suitable superpositions of
X-waves, which are a natural extension of Bessel beams in the pulsed domain.
Moreover, we show, that while field rotating RSAPs preserve their
self-acceleration character, intensity rotating RSAPs only possess pseudo
self-acceleration, as their transverse intensity distribution is deformed
during propagation, due to their propagation-dependent angular velocity.
