No need to check for UPDATE, DELETE or INSERT.

Trigger is designed for UPDATE.

Also, the trigger is nesting itself by updating the table for which the trigger ís triggering on...

Use this

CREATE TRIGGER[dbo].[TG_U_UpdTable]

ON[dbo].[UpdTable]

AFTERUPDATE

AS

IF UPDATE(db_updateDate) OR UPDATE(db_updateBy)

RETURN

UPDATEd

SETd.db_updateDate = GETDATE(),

d.db_updateBy = SYSTEM_USER

FROMdbo.UpdTable AS d

INNER JOINinserted AS i ON i.UpdTableOID = d.UpdTableOID