Almost a unit root

I am working on a monetary union model and found 2 eigenvalues which are very close to one (printed as 1 they are actually 0.99999).
The rank condition is otherwise satisfied are there is capital depreciation and debt premia (as in Schmitt Grohe and Uribe).
I wonder whether I can trust that the model returns to SS (in a few hundred iterations) or wheter this eignevalue could be real ones found slightly smaller due to numerical computations.

Best regards,
Aurélien Poissonnier

I found the problem, it was on the relative price of domestic goods and imported goods.
So in the check list when unit roots appear I have :
1 non zero capital depreciation
2 price level or inflation
3 in open eco some feature to ensure that financial positions converge (debt premia or other)
4 relative prices of imports and domestic goods