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{Timing analysis of Accretion-powered Millisecond Pulsars (AMPs) is apowerful tool to probe the physics of compact objects. The recently discovered\newigrj is the 12 discovered out of the 13 AMPs known. The Rossi XTE satelliteprovided an extensive coverage of the 25 days-long observation of the sourceoutburst.} {Our goal is to investigate the complex interaction between theneutron star magnetic field and the accretion disk, determining the angularmomentum exchange between them. The presence of a millisecond coherent fluxmodulation allows us to investigate such interaction from the study of pulsearrival times. In order to separate the neutron star proper spin frequencyvariations from other effects, a precise set of orbital ephemeris ismandatory.} {Using timing techniques, we analysed the pulse phase delaysfitting differential corrections to the orbital parameters. To remove theeffects of pulse phase fluctuations we applied the timing technique alreadysuccessfully applied to the case of an another AMP, XTE J1807-294.} {We reporta precise set of orbital ephemeris. We demonstrate that the companion star is amain sequence star. We find pulse phase delays fluctuations on the firstharmonic with a characteristic amplitude of about 0.05, similar to what alsoobserved in the case of the AMP XTE J1814-338. For the second time an AMP showsa third harmonic detected during the entire outburst. The first harmonic phasedelays show a puzzling behaviour, while the second harmonic phase delays show aclear spin-up. Also the third harmonic shows a spin-up, although not highlysignificant (3$\sigma$ c.l.). The presence of a fourth harmonic is alsoreported. In the hypothesis that the second harmonic is a good tracer of thespin frequency of the neutron star, we find a mean spin frequency derivativefor this source of \np{1.65(18)}{-13} Hz s$^{-1}$.} (continue ...)

Timing of the accreting millisecond pulsar IGR~J17511--3057