Hello!

I have Debian 8 and 2 wi-fi routers.
My target is connect to both routers the same time, to have 2 network interfaces.

I did create virtual network interface and change its MAC address (simple increment):

rename8 IEEE 802.11bgn ESSID: "POINT_1"
Mode: Managed Frequency: 2.412 GHz Access Point: 01: 17: 9A: 72: 43: AC
Bit Rate=54 Mb/s Tx-Power=14 dBm
Retry short limit: 7 RTS thr: off Fragment thr: off
Encryption key: off
Power Management: off
Link Quality=46/70 Signal level=-64 dBm
Rx invalid nwid: 0 Rx invalid crypt:0 Rx invalid frag: 0
Tx excessive retries: 0 Invalid misc: 11251 Missed beacon: 0

wlan0 IEEE 802.11bgn ESSID: off/any
Mode: Managed Access Point: Not-Associated Tx-Power=14 dBm
Retry short limit: 7 RTS thr: off Fragment thr: off
Encryption key: off
Power Management: off

Btw, I created "wlan1" name but it shows as "rename8"

I can connect to both points from each interface separately.
But when I'm trying to connect both the same time, 2nd interface trying to connect some time and then fails.

1st router use channel #1
2nd not sure, it's ASUS, it has "auto/36/40/44/48", I tried auto and 44. It does not help.

02: 00.0 Network controller: Qualcomm Atheros AR9285 Wireless Network Adapter (PCI-Express) (rev 01)

Also, I wonder how to know if my controller supports parallel connections.

Please help to solve this

I can see issues (e.g. wpa_supplicant) if you're the client. If you're the server, then it's workable. There's not enough info in your post for us to have a go at answering this.

Has a similar setup worked in linux for you before, or are you trying your luck?
Have you 2 internet connections? Are you trying for extra speed or something? There's (kernel) network interface bridging technology; I think it's cable only but you can read up & check. You would probably need the same wpa_supplicant key on both routers. Bridging is not the sort of thing that would necessarily be enabled by default in a kernel.

I am the client, not server
I want to have 2 interfaces to use them in different virtual machines. Cause each router provides different IP

mobile internet - router1 ssid POINT_1 - my PC - wlan0 interface - virtual machine #1
home network - router2 ssid POINT_2 - my PC - rename10 interface - virtual machine #2

Also I just notice these records:

dmesg -w:

[63578.395746] ICMPv6: NA: someone advertises our address fe80:0000:0000:0000:e2df:9aff:fe16:67e2 on wlan0!
[63590.671808] rename10: authenticate with 70:8b:cd:e9:a2:f8
[63602.081778] rename10: authenticate with 70:8b:cd:e9:a2:f8
[63614.391170] rename10: authenticate with 70:8b:cd:e9:a2:f8
[63626.701351] rename10: authenticate with 70:8b:cd:e9:a2:f8
[63639.002567] rename10: authenticate with 70:8b:cd:e9:a2:f8
[63951.958220] rename10: authenticate with 70:8b:cd:e9:a2:f8

daemon.log:

c 24 19:34:31 host wpa_supplicant[1108]: rename10: SME: Trying to authenticate with 70:8b:cd:e9:a2:f8 (SSID='POINT_2' freq=2467 MHz)
Dec 24 19:34:31 host wpa_supplicant[1108]: rename10: SME: Authentication request to the driver failed
Dec 24 19:34:31 host wpa_supplicant[1108]: rename10: CTRL-EVENT-SSID-TEMP-DISABLED id=0 ssid=«POINT_2» auth_failures=1 duration=10 reason=CONN_FAILED
Dec 24 19:34:32 host NetworkManager[22970]: <info> (rename10): supplicant interface state: scanning -> disconnected

I am not the world's expert, but wpa_supplicant cannot deal with 2 authentication keys at once AFAIK. How does it know which packet is encrypted with which key? In the situation you describe, at least one of the VMs are going to have to handle the network interface hardware directly.

At least one VM is going to have to run all the wifi stuff (dhcp, wpa_supplicant, wifi driver in the kernel, firmware, whatever) and I foresee issues there. VMs normally take the system network connection, and the other one can do that.

How about trying that? Disable one wifi adapter (the slower one) in the main system; disable system internet on one vm and try to connect to the (disabled) wifi adapter. I expect there will be a good reason why this will not work. In that case, the lyrics of Fagan in "Oliver Twist" apply:

"I think I'd better think it out again!"