  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.
