THE CAPT OF A B737 TAXIES HIS ACFT'S #1 ENG INTO A TUG DURING THE RAMP DEP PROC AT SJC; CA.

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AS CAPT OF THIS FLT; I CALLED FOR AND COMPLETED THE BEFORE START CHKLIST AND THEN RELEASED BRAKES AND CLRED THE TUG OPERATOR TO COMMENCE PUSHBACK FOR OUR FLT. THE PUSHBACK CREW WAS FROM ANOTHER ACR UNDER CONTRACT AND CONSISTED OF THE TUG OPERATOR WHO WAS ON HEADSET AND 1 WING WALKER INSTEAD OF OUR USUAL 2. AS THE PUSHBACK WAS IN PROGRESS; THE FO AND I STARTED THE #1 ENG AND THEN THE #2 ENG. THE ACFT WAS PUSHED BACK WITH A 90 DEG TURN TO ALIGN US ON A TXWY AND WHEN PUSHBACK WAS COMPLETE; I SET THE BRAKES AT THE TUG OPERATOR'S REQUEST. I THEN CLRED HIM TO DISCONNECT THE TOW BAR AND HEADSET AND TOLD HIM I'D SEE HIM OUT FRONT. I CALLED FOR THE AFTER START CHKLIST WHICH THE FO AND I PERFORMED ALONG WITH OUR USUAL PANEL SCANS. I HEARD THE NORMAL 'CLUNK' OF THE TOW BAR BEING DISCONNECTED AND THE 'CLICK' OF THE COMS DOOR BEING CLOSED. ALSO IN MY PERIPHERAL VISION; I THOUGHT I SAW THE TUG INITIATE MOVEMENT BACK FROM THE ACFT AND THE MARSHALLER WALK A FEW STEPS AWAY FROM THE ACFT WITH HER BACK TO ME. I FLASHED THE TAXI LIGHT FOR THE TUG OPERATOR SIGNALING THAT I WAS READY TO TAXI. AT THAT POINT; I CALLED FOR THE FO TO SELECT FLAPS 5 DEGS AND CALL FOR TAXI CLRNC. WE WERE THEN CLRED BY GND CTL TO TAXI TO RWY 30L AFTER AN MD80 PASSED US ON OUR R SIDE ON A PARALLEL TXWY. I ASKED THE FO IF HE SAW THE MD80 AND HE LOOKED TO HIS R AND SAID HE SAW THE MD80 COMING; BUT IT WAS SOME DISTANCE BACK YET. I WAITED UNTIL I SAW THE OTHER ACFT PASS OUR R AND THEN SCANNED IN FRONT OF AND TO THE R OF OUR ACFT AND SAW NO HAZARDS. I THOUGHT I MUST HAVE MISSED THE TAXI SALUTE FROM THE MARSHALLER AND BOTH WERE WELL CLR AND PROBABLY ALREADY BACK AT THE GATE. I COMMENCED TO TAXI AND SHORTLY THEREAFTER FELT THE ACFT SHUDDER AND STOP. WE HAD CONTACTED THE TUG WITH THE #1 ENG. AFTER MY INITIAL SHOCK AT WHAT HAD HAPPENED; I TOLD THE FO TO NOTIFY GND CTL OF WHAT HAD HAPPENED AND TO REQUEST THAT EMER EQUIP BE DISPATCHED TO OUR LOCATION AS A PRECAUTION. I PERFORMED APPLICABLE PARTS OF THE ENG FIRE ON GND CHKLIST TO SHUT DOWN THE ENGS AND SECURE THE ACFT FROM FURTHER DAMAGE; MADE A SHORT PA TO THE PAX; AND CALLED OPS ON THE RADIO TO INFORM THEM WHAT HAD HAPPENED AND ASKED THEM TO NOTIFY THE COMPANY. PAX WERE DEPLANED VIA STAIRS AND RETURNED TO THE TERMINAL. THANKFULLY; NO INJURIES WERE INCURRED BY ANYONE. FACTORS CONTRIBUTING TO THIS MISHAP WERE THAT PUSHBACK WAS MADE WITH A CONTRACT CREW FROM ANOTHER AIRLINE THAT USED ONLY 2 PEOPLE INSTEAD OF 3. THAT LED TO A SIT WHERE NO ONE WAS OUT IN FRONT OF THE ACFT TO BE VISIBLE AND GIVE A STOP SIGNAL AT A CRITICAL TIME WHEN BOTH THE TUG OPERATOR AND THE MARSHALLER WERE UNDER THE NOSE OF THE ACFT OUT OF SIGHT OF THE COCKPIT CREW. ADDITIONALLY; I WAS DISTR FROM MY NORMAL OUTSIDE VIGILANCE BY LOOKING FOR ANOTHER ACFT TO FOLLOW AND THAT DREW MY ATTN AWAY FROM THE FRONT OF THE ACFT. MOST IMPORTANT; HOWEVER; WAS THE FACT THAT I ASSUMED THAT I MUST HAVE BEEN CLR TO TAXI WHEN I SAW NOTHING IN FRONT OF THE ACFT. MORAL: NEVER EVER TAXI AN ACFT WITHOUT A DEFINITE 'CLR TO TAXI' SIGNAL FROM YOUR MARSHALLER. THINGS MAY NOT BE WHERE YOU THINK THEY AREA. IT CAN HAPPEN TO YOU!