Context : The Red MSX Source ( RMS ) survey is an ongoing multi-wavelength observational programme designed to return a large , high-resolution mid-infrared colour-selected sample of massive young stellar objects ( MYSOs ) .
We have identified \sim 2000 MYSO candidates located within our Galaxy by comparing the colours of MSX and 2MASS point sources to those of known MYSOs .
The aim of our follow-up observations is to identify other objects with similar colours such as ultra compact ( UC ) HII regions , evolved stars and planetary nebulae ( PNe ) and distinguish between genuine MYSOs and nearby low-mass YSOs .

Aims : A critical part of our follow-up programme is to conduct ^ { 13 } CO molecular line observations in order to determine kinematic distances to all of our MYSO candidates .
These distances will be used in combination with far-IR and ( sub ) millimetre fluxes to determine bolometric luminosities which will allow us to identify and remove nearby low-mass YSOs .
In addition these molecular line observations will help in identifying evolved stars which are weak CO emitters .

Methods : We have used the 15 m James Clerk Maxwell Telescope ( JCMT ) , the 13.7 m telescope of the Purple Mountain Observatory ( PMO ) , the 20 m Onsala telescope and the 22 m Mopra telescope to conduct molecular line observations towards 508 MYSOs candidates located in the 1st and 2nd Quadrants .
These observations have been made at the J =1–0 ( Mopra , Onsala and PMO ) and J =2–1 ( JCMT ) rotational transition frequency of ^ { 13 } CO molecules and have a spatial resolution of \sim 20″–55″ , a sensitivity of T _ { A } ^ { * } \simeq 0.1 K and a velocity resolution of \sim 0.2 km s ^ { -1 } .
We complement these targeted observations with ^ { 13 } CO spectra extracted from the Galactic Ring Survey ( GRS ) , which have a velocity resolution of \sim 0.21 km s ^ { -1 } and sensitivity T _ { A } ^ { * } \simeq 0.13-0.2 K , towards a further 403 RMS sources .

Results : In this paper we present the results and analysis of the ^ { 13 } CO spectra obtained towards 911 MYSO candidates .
We detect ^ { 13 } CO emission towards 780 RMS sources which corresponds to approximately 84 % of those observed .
A total of 2595 emission components are detected above 3 \sigma level ( typically T ^ { * } _ { A } \geq 0.3 K ) , with multiple components being observed towards the majority of these sources – 520 sources ( \sim 56 % ) – with an average of \sim 4 molecular clouds detected along each line of sight .
These multiple emission features make it difficult to assign a unique kinematic velocity to many of our sample .
We have used archival CS ( J =2–1 ) and maser velocities to resolve the component multiplicity towards 175 sources ( \sim 20 % ) and have derived a criterion which is used to identify the most likely component for a further 191 multiple component sources .
Combined with the single component detections we have obtained unambiguous kinematic velocities for 638 of the 780 MYSOs candidates towards which CO is detected ( \sim 80 % of the detections ) .
The 141 sources for which we have not been able to determine the kinematic velocity will require additional line data .
Using the rotation curve of Brand and Blitz ( 1993 ) and their radial velocities we calculate kinematic distances for all detected components .

Conclusions :