Connection from/to a LAN computer even after its address being blocked

Hi all,
I noticed that there are several connections (inbound and outbound) to my computer from a few specific computers over our LAN. There was a continuous flow over ports 445 and 139 with a data rate of the order of MB/s. I tried to terminate the connections several times but they were back in no time. Then I defined some “Global Rules” to block any connection from/to those computers. To my surprise those connections were still alive but now with a data rate of a few kB/s. Now what do you think? How can I identify the source of the problem. The process responsible for those connections was “System”.