Engine stalling or failure to start may indicate crankshaft angle sensor failure; Hyundai issued a recall (03V030000).
Problems for specific Hyundai Santa Fe years:
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Repairpal verified 2001 Hyundai Santa Fe problems
The crankshaft position sensor may fail, causing engine stalling or a failure to start. Replacement or the failed sensor will commonly correct this problem.
Prior to replacing the automatic transmission fluid (to improve shift quality), make sure that the transmission fluid level is correct. Also, make sure the computer that controls the transmission has the most up-to-date adaptive programming information. When servicing these transmissions be sure to use fluid approved by Hyundai.
The timing belt can fail prematurely; if it fails while driving, it can cause catastrophic damage to the engine. Be sure that the timing belt is inspected and replaced according to the manufacturer's recommended schedule.