You need to remove polys where they touch then weld the vertices together. This does mean you will need the same number of vertices on both parts in the ithe appropriate locations. If you want them to stay in their current positions (relative to each other) you could select the 2 Borders (caused by removing the facing polys) and Bridge them.
A screenshot, or a copy of the scene (zipped), would help as we don't know what the 2 elements look like or how they need to be joined together.
Also, please make sure you always state your Max version - if you put this in your sig then you can't forget - as it can sometimes be important.
Max 2016 (SP1/EXT1)
Win7Pro x64 (SP1). i5-3570K @ 4.4GHz, 8Gb Ram, DX11.
nVidia GTX760 (2GB) (Driver 430.86).