I have several line text-files of (used in GMT) saved in the format (this is a small sample):

    -111.29 42.28
    -111.29 42.31
    -111.29 42.33
    >
    -111.37 41.99
    -111.38 42.02

I am trying to convert this to a Shape file to use in QGIS. I know people convert from shp to GMT with ogr2ogr can you do this in reverse Gmt to Shp? I tried using ogr2ogr and had no luck. Maybe I did something wrong or it is not possible with that tool. Any help would be much appreciated!  

Also - I have tried to import this format in Qgis via the delimited text layer tool, but can only figure out how to get points when i need lines.