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Aside from certain occupations in agriculture, and the entertainment industry (child actors), children younger than 14 may not be employed by companies; children younger than 14 may be employed directly by their parents in occupations other than manufacturing or mining (hazardous duty prohibitions still apply, though - see below)
Child actors under 14 may be employed under special rules with submission of a valid authorization form (available at http://www.twc.state.tx.us/ui/lablaw/llcl73.pdf (PDF))
No hazardous duties for any child younger than 18 - a complete list of hazardous duty categories is at http://www.twc.state.tx.us/ui/lablaw/llcl70.pdf (PDF)
Limitations on hours of work for children who are 14 or 15:
No work during school hours
No more than three hours during a school day, or more than 18 hours in a school week
No more than eight hours during a non-school day, or more than 40 total hours during a non-school week
No work between 7:00 p.m. and 7:00 a.m. during the school year
If not enrolled in summer school, 14- and 15-year olds may work between 7:00 a.m. and 9:00 p.m. from June 1 through Labor Day
If interstate commerce is not involved, and the FLSA does not apply, then Texas law provides that 14- and 15-year olds may work no more than 8 hours per day and no more than 48 hours in a week; may not work between 10:00 p.m. and 5:00 a.m. before a school day; may not work between midnight and 5:00 a.m. before a non-school day; and may not work between midnight and 5:00 a.m. during the summer recess
There are no limitations on hours of work for children who are 16 or 17
Children are entitled to minimum wage and overtime pay
Sub-minimum wage of $4.25/hour is permissible during the first 90 days in a job
Children who are tipped employees may be paid the same as other tipped employees
Other sub-minimum wages (generally, 85% of the current minimum wage) may be permissible under special certificates issued by DOL for certain student employees and apprentices
Normal payroll tax laws apply to children, just as they do to workers over 18
If possible, secure permission from child's parent to employ anyone under age 18
Special training is advisable for management regarding harassment issues if the business employs children; complaints from employees younger than 18 should receive top priority for resolution; certain offenses (assault, improper photography, etc.) may need to be reported to law enforcement
Penalties for child labor law violations:
Texas law - civil penalties up to $10,000 per violation; criminal penalties for Class A and B misdemeanors; injunctive relief
Federal law - civil penalties up to $11,000 per violation ($50,000 for death or serious injury to a minor employee - $100,000 for repeated or willful violations of that type); criminal penalties (up to a $10,000 fine per violation and/or imprisonment); injunctive relief; prohibition on sale or transfer of any goods produced by the employer at the time of, or within 30 days after, a child labor violation (such goods are also known as "hot goods")