10.0.0.0, 172.16.0.0 and 192.168.0.0 network spaces are the private network spaces (http://en.wikipedia.org/wiki/Private_network).

Check the default gateway on a computer with a 10.61.X.X address. Put that address in a browser and see what you get. You can have more than one DHCP server answering requests. Clients will pull IPs from whichever answers the quickest. If devices are pulling addresses from both routers, your Netgear is bleeding somehow onto your private network.

Routers in their default configuration will NAT all traffic from the private network space to the public space (http://whatismyipaddress.com/nat). The Internet side of your of your Linksys router should be in a different IP address space than the private side of your network.