# Is a bond expiring at $T$ clean or dirty price a martingale under the $T$-Forward measure?

When we say Bond prices are martingale under T-Forward measure, do we mean their Clean Price is a martingale or is it their dirty price.

I guess it should be dirty price, as clean price is just a convenient representation while dirty price is the actual price of the bond. But it will be great if somebody could please validate/invalidate my thoughts.

Your question is not really clear. Why do you need the bond price to be a martingale under the $T$-forward measure? The $T$-forward measure is used mainly for modelling the LIBOR rate. Note that, the bond price itself is not a martingale; instead, the bond price relative to the $T$-maturity zero coupon bond price is a martingale.