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As it stands, we can't give you a definitive answer about what these connections may be. What that netstat snippet tells us is that you have something running on your local server that is using either port 60666 or 35325 as an unprivileged source port, and is then connecting to some service that is running on the other unprivileged destination port.
A better bet on Linux might be to look at the output of netstat -lntp specifically, as this will show you which ports are in a listening state, and also what processes or services are specifically responsible for those connections. Likewise netstat -ntp will show you the processes or services for all TCP connections, where these are known (or knowable).