  We report on two RossiXTE observations of the anomalous X-ray pulsars 1E
1048.1-5937 and 1E 2259+586. Both sources have continued their almost constant
spin-down during 1995/96. We carried out a search for orbital Doppler shifts,
in their observed spin frequencies, deriving stringent limits on the projected
semi-axis. Unless these systems have unlikely small inclinations, main sequence
companions can be excluded. If 1E 1048.1-5937 and 1E 2259+586 are indeed binary
systems, their companion stars must be either white dwarfs, or helium-burning
stars with M < 0.8 Msolar, possibly underfilling their Roche lobe.
