Using X-ray data from the Rossi X-Ray Timing Explorer ( RXTE ) , we carried out pulse timing analysis of the transient X-ray pulsar SAX J2103.5+4545 . An outburst was detected by All Sky Monitor ( ASM ) October 25 1999 and reached a peak X-ray brightness of 27 mCrab October 28 . Between November 19 and December 27 , the RXTE/PCA carried out pointed observations which provided us with pulse arrival times . These yield an eccentric orbit ( e= 0.4 \pm 0.2 ) with an orbital period of 12.68 \pm 0.25 days and light travel time across the projected semimajor axis of 72 \pm 6 sec . The pulse period was measured to be 358.62171 \pm 0.00088 s and the spin-up rate ( 2.50 \pm 0.15 ) \times 10 ^ { -13 } Hz s ^ { -1 } . The ASM data for the February to September 1997 outburst in which BeppoSAX discovered SAX J2103.5+4545 ( Hulleman , in ’ t Zand and Heise 1998 ) are modulated at time scales close to the orbital period . Folded light curves of the 1997 ASM data and the 1999 PCA data are similar and show that the intensity increases at periastron passages . Subject headings : binaries : close – pulsars : individual : SAX J2103.5+4545 – stars : neutron – X-rays : stars