PLT DSNDED 700 FT WITHOUT ATC CLRNC.

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ENRTE FROM GRAND CAYMAN TO DALLAS FT WORTH ON MAY/XX/94 AT XA30 LCL TIME; WE RECEIVED A 'HOLD' AT COIAX INTXN WITH AN EXPECT FURTHER CLRNC TIME OF XE50. THE WX IN THAT AREA WAS POOR. CONTINUOUS MODERATE TURB; ICING. WE WERE HAVING A PROB RECEIVING SCURRY; VOR (SCY) DUE TO THAT; PLUS LARGE TSTM (CELL) CLOSE TO HOLD FIX. AFTER 1 TURN IN THE HOLD WE REALIZED THAT OUR FUEL DID NOT ALLOW TO HOLD MUCH LONGER THAN THE 'EFC' TIME. WE DECIDED TO DIVERT TO WICHITA FALLS; TX; (ICT). WE WERE AT FL210. WITH THE WX SIT AS IT WAS WE ASKED FOR 'HIGHER.' WE WERE THEN CLRED TO FL220. SHORTLY AFTER LEVEL OFF AT FL220 (AROUND THE 030 DEGS AND 20 DME FROM SCURRY VOR) (SCY) AREA; WE RECEIVED A TCASII RA. 'DSND;' AND THE TCASII IVSI INDICATED A DSCNT OF ABOUT 2500 FPM. WE BEGAN OUR DSCNT. AT ABOUT FL215 ZFW CALLED TO ASK ABOUT OUR ALT. WE ADVISED THAT WE WERE IN A TCASII RA DSCNT. ANOTHER AIRLINES ALSO SAID 'SO IS OTHER ACR NUMBER?' ON A TCASII ADVISORY. WE DSNDED TO FL213. AFTER THE TFC CONFLICT; WE CLBED BACK TO FL220 AND PROCEEDED ON COURSE. AT THIS POINT; I DO NOT KNOW WHAT COULD HAVE CAUSED THIS TFC PROBLEM AND TCASII RA. MY GUESS IS THAT THE OTHER ACR MAY HAVE BEEN CLRED ABOVE US WITH A HIGH RATE OR CLIMB OR CLRED TO FL210 WITH A HIGH RATE OF CLB. POSSIBLY WE WERE BOTH CLRED TO MAINTAIN FL220.