ZMP Controller described a confused descent clearance situation; claiming same company similar call signs were the primary causal factor; adding airlines should make efforts to reduce similar flight numbers during the same time frames.

Narrative

I had been in the RADAR position for approximately 15-20 minutes and didn't recognize two aircraft with similar sounding call signs. I put Air Carrier XXXX on a vector for sequencing MSP arrivals. He accepted the clearance. A few minutes later the Conflict Alert went off and I resumed Air Carrier XXXX on course and a descent to FL280. He responded but did not turn or descend. I gave Air Carrier XXXX a further descent; told him of his company traffic and to resume on course. He once again acknowledged. I still did not see the aircraft descend so I turned his company over FSD that was also at FL310 to a 90 heading and asked again. Air Carrier YXXX responded saying I have been doing everything you asked! It was then that I realized the similar sounding call signs and was able to give the correct call sign all the clearances I had been giving to Air Carrier YXXX instead of Air Carrier XXXX. I would appreciate the airlines not giving aircraft landing at the same airport at the same time similar sounding call signs!! Luckily Air Carrier YXXX was on course and had previously been given a descent clearance. I would recommend that airlines not use similar sounding call signs for aircraft landing the same airport at the same time. This has been an issue since a recent merger and now it has resulted in what could have been a major disaster!