Aims. We present the first long-term pulse profile study of the X-ray pulsar SAX J2103.5+4545. Our main goal is to study the pulse shape correlation either with luminosity, time or energy. Methods. This Be/X-ray binary system was observed from 1999 to 2004 by RXTE PCA, and by INTEGRAL from 2002 to 2005, during the Performance and Verification (PV) phase and the Galactic Plane Scan survey (GPS). X-ray pulse profiles were obtained in different energy ranges. The long-term spectral variability of this source is studied. The long-term flux, frequency and spin-up rate histories are computed. A new set of orbital parameters are also determined. Results. The pulse shape is complex and highly variable either with time or luminosity. However, an energy dependence pattern was found. Single, double, triple or even quadruple peaks pulse profile structure was obtained. It was confirmed that SAX J2103.5+4545 becomes harder when the flux is higher. The new orbital solution obtained is: P_orb= 12.66528+-0.00051 days, e = 0.401+-0.018, w = 241.36+-2.18 and a_xsin i = 80.81+-0.67 lt-s.
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