B757-200 FLT CREW RECEIVES EICAS BRAKE SOURCE AND R SYS PRESSURE ANNUNCIATIONS DURING CLIMBOUT. DECLARE EMERGENCY AND RETURN.

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DURING CLBOUT 'R SYS PRESSURE;' 'BRAKE SOURCE' ANNUNCIATOR LIGHTS AND AMBER EICAS MESSAGES APPEARED. R QUANTITY AND PRESSURE INDICATIONS NORMAL ON STATUS PAGE. PERFORMED QRH PROCS; TURNED OFF R HYD PUMPS; DECLARED EMER AND TURNED BACK TOWARDS ZZZ. CONTACTED DISPATCH; CIRCLED NEAR ZZZ1 AT 3000 FT WITH GEAR DOWN; FLAPS 20 DEGS; SPD BRAKE EXTENDED TO BURN DOWN FROM 206000 LBS TO 195000 LBS. FLT ATTENDANTS PERFORMED PLANNED EVAC CHKLIST. DECIDED TO PROCEED INBOUND AS DAYLIGHT WAS FADING. ON APCH; PERFORMED BRAKE SOURCE QRH PROC; PUSHING RESERVE BRAKES SWITCH. BRAKE SOURCE ANNUNCIATOR AND EICAS LIGHTS THEN EXTINGUISHED; FOLLOWED ABOUT 2 MINS LATER BY 'R SYS PRESSURE' ANNUNCIATOR AND EICAS EXTINGUISHING. I HAD REQUESTED THE ARPT FIRE TRUCKS; ETC; TO BE STANDING BY. TOUCHED DOWN AT 500 FT POINT ON RWY; STOPPED ACFT BY INTXN. TAXIED CLR OF RWY AS ALL SYS APPEARED TO BE WORKING NORMALLY. MAINT CHKED BRAKES AND I TURNED RESERVE BRAKES SWITCH OFF AND AS ALL SEEMED TO BE WORKING NORMALLY I WAS CLRED BY MAINT TO PROCEED TO GATE.