AN ACR MLG HAD MULTIPLE ACFT EQUIP PROBS #1 COMPASS SYS INOP; #2 COMPASS SYS VERY SLOW TO SLEW; AND FAILURE FLAGS ON BOTH SYS INOP.

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DEPARTING ORD DURING BUSY TIME. ASSIGNED HDG FOR RADAR VECTORS EVERYTHING IN COCKPIT APPEARS NORMAL. ORD DEP ASKS US WHAT HDG WE ARE FLYING. WE WERE ASSIGNED 205 DEGS AND BOTH COMPASS SYS SHOWED THAT. DEP CTL ADVISED US THAT WE WERE TRACKING SOMETHING FAR DIFFERENT (ABOUT 250 DEGS). THE FO AND I XCHKED EACH OTHER'S COMPASSES; HSI AND RMI. THEY ALL AGREED AND NO WARNING FLAGS OR FAILURE LIGHTS WERE IN VIEW. WE CHKED THE STANDBY COMPASS AND IT SHOWED ABOUT 240 DEGS; WHICH AGREED WITH THE CTLR'S INFO AND NOT WITH OUR 2 COMPASSES. WE ADVISED DEP CTL OF OUR NAV PROB AND REQUESTED A GYRO-OUT TURN TO THE HDG HE NEEDED. AFTER ACCOMPLISHING THIS; WE TROUBLESHOT THE SYS. WE DETERMINED THAT THE #2 COMPASS SYS WAS VERY SLOW TO SLEW; BUT AFTER WINGS LEVEL; IT DID BECOME REASONABLY ACCURATE (ABOUT 8-10 DEG ERROR). THE #1 COMPASS SYS WAS INOP. THE FLAGS AND FAILURE LIGHTS ON BOTH SYS WERE INOP. THE STANDBY SYS WAS OK. WE ADVISED ZAU OF OUR LIMITED NAV CAPABILITIES. THE WX AT IAH WAS VFR. WE CONTINUED TO IAH WITH GYRO OUT HDGS. WE HAD A GOOD STANDBY AND THE #2 COMPASS ERROR WAS A KNOWN QUANTITY. UNEVENTFUL LNDG.