On-the-run

In the Treasury market, describes the most recently auctioned 2, 3, 5, 10 and 30-year bonds. For purposes of quoting corporate bonds in spread, the nearest on-the-run Treasuries are almost always used. Liquidity tends to be slightly better in on-the-run issues, and it also tends to be easier to short-sell on-the-run issues.

Bond market pros will refer to the on-the-run Treasuries generically by the number of years to maturity. For example, "the 10 year" or even just "10s" is often used to mean the most recently auctioned 10-year issue.

Example
I can bid Merrill Lynch '15's at +89 vs 10's. (Translation: This person is offering to buy Merrill Lynch bonds maturing in 2015 at a yield equal to 89bps greater than the on-the-run 10-year Treasury.)

In corporate and agency bonds, on-the-run refers to large issues which trade frequently. There is no official means of defining what issues are on-the-run versus not. It is whatever issues tend to be favored by traders. Usually issues considered on-the-run have maturities centered around 5, 10, and 30-years. Similarly, most on-the-run issues have bullet maturities. Also bonds deliverable into CDS contracts for large issuers are common on-the-run issues.

Any other issue is considered "off-the-run."