If I claim zero allowances on both my W4s, how can I owe federal taxes?

[SweetieJean]

Do you have income other than wages?

[gabnalgus]

No

[gabnalgus]

One income is a job I am currently working and the other is my monthly annuity.

[gabnalgus]

I had the same situation last year and received a refund.

[SweetieJean]

Well, your credits such as (EIC) may have been different. Look at 2016 and 2017 side by side. Also check your data entry.

[SweetieJean]

Your annuity is not a wage. 

But each withholding (say, 15%) is calculated as if is your only income.  When you add them together, you can end up in  higher tax bracket (say, 25%).

https://apps.irs.gov/app/withholdingcalculator/

https://www.irs.gov/pub/irs-pdf/fw4p.pdf