AN ACR E120 FLC LANDED ON RWY 18L; THEN; WITHOUT AUTH; CROSSED RWY 18R.

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TUL TWR WAS HANDLING TWR AND GND FREQS. MY RECOLLECTION IS THAT THERE WERE 1 OR 2 ACFT ALOFT; AND 1 OR 2 ON THE GND EXCLUDING OUR FLT; ALL COMMUNICATING ON FREQ. THE FREQ WAS NOT CONGESTED; HOWEVER. WE LANDED ON RWY 18L; I WAS PF; CAPT TOOK CTL OF ACFT AND EXITED RWY 18 AT SECOND HIGH SPD. TWR WAS DEPARTING ANOTHER ACR (B737) ON OUR RWY 18L AS WE CLRED. CAPT CALLED FOR AFTER LNDG CHKLIST AND AS I COMPLETED IT; I ADVISED TWR THAT WE WERE 'CLR OF RWY 18L;' TWICE. IT BECAME OBVIOUS TO ME THAT THE CAPT WAS XING THE E/W RWY WHETHER TWR RESPONDED OR NOT. IT WOULD HAVE BEEN AN ABRUPT STOP TO HOLD SHORT SINCE THAT HIGH SPD TXWY IS SHORT. I VISUALLY CHKED FOR TFC; AS DID THE CAPT; AS WE APCHED AND CROSSED THE RWY. THE CAPT SAID SOMETHING LIKE; 'I GUESS WE'RE XING.' I MADE NO FURTHER CALLS TO TWR; NOR THEM TO US. WE PROCEEDED WITHOUT INCIDENT TO THE GATE. IT IS COMMON FOR THIS AND OTHER TWRS TO CLR US TO LAND AND TAXI TO THE GATE AT ONCE; BUT THAT DID NOT OCCUR THAT EVENING. BASED ON THE COMS I HEARD ON FREQ; AND A VISUAL CHK; I WAS NOT CONCERNED ABOUT A RWY INCURSION; ONLY THE ISSUE OF XING WITHOUT ATC CLRNC. HAD I INTERVENED AND APPLIED THE BRAKES TO HOLD SHORT BY THE TIME I REALIZED THE CAPT WAS NOT GOING TO STOP; IT WOULD HAVE BEEN A VERY ABRUPT STOP; POSSIBLY RESULTING IN SKIDDING; ETC. I BELIEVE THE CAPT WAS DOING WHAT WE ALMOST ALWAYS DO WHEN LNDG AT TUL ON RWY 18L; AND I BELIEVE TWR WAS BUSY GETTING THE B737 OUT AND MISSED MY CALLS. I THINK THE CAPT SHOULD HAVE BEGUN SLOWING DOWN WHEN MY FIRST CALL TO TWR WAS NOT ACKNOWLEDGED. FOR THE RECORD; THIS WAS OUR LAST LEG OF A 6 HR DAY (3 HRS BLOCK TIME). NO SIGNIFICANT WX OR DELAYS; ETC.