X-ray observations of the accreting X-ray pulsar 4U 1907 + 09 obtained during 1996 February with the Proportional Counter Array onboard the Rossi X-Ray Timing Explorer (RXTE) have made possible the first measurement of the intrinsic pulse period (P-pulse) since 1984: P-pulse = 440.341(-0.017)(+0.012) s. 4U pulse 1907 + 09 is in a binary system with a blue supergiant. The orbital parameters have been solved, which enables us to correct a measurement of P-pulse obtained in 1990 with Ginga for orbital delay effects. Thus, three spin-down rates can be extracted from four pulse periods obtained in 1983, 1984, 1990, and 1996. These are equal to within 8% to a value of (P) over dot(pulse) = +0.225 s yr(-1). This suggests that the pulsar has perhaps been in a monotonous spin-down mode since its discovery in 1983. Furthermore, the RXTE observations showed transient similar to 18 s oscillations during a flare that lasted about 1 hr. These oscillations could be interpreted as Keplerian motion of an accretion disk near the magnetospheric radius. This, and the notion that the corotation radius is much larger than any conceivable value for the magnetospheric radius (because of the long spin period), renders it unlikely that this pulsar spins near equilibrium, as is suspected for other slowing accreting X-ray pulsars. We suggest as an alternative that the frequent occurrence of a retrograde transient accretion disk may be consistently slowing the pulsar down. Further observations of flares could provide more evidence of this.