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                                                                    EXHIBIT 23.1
 
                   CONSENT OF INDEPENDENT PUBLIC ACCOUNTANTS
 
     As independent public accountants, we hereby consent to the use of our
report on the combined financial statements of Northern Line Layers, Inc. dated
March 19, 1999 in this Current Report on Form 8-K/A of Quanta Services, Inc. and
to the incorporation by reference of said report into Quanta Services, Inc.'s
previously filed Registration Statements on Form S-8 (File Nos. 333-47069 and
333-56849).
 
ARTHUR ANDERSEN LLP
 
Houston, Texas
April 21, 1999