Thanks Daniel for your usual help, it is really appreciated !

I've inserted the following block on the failure route: 
        if (t_check_status("401|407")) {
                xlog("L_INFO","failure_route(ROUTEFAIL) @@ call to uac_auth()\n");
                uac_auth();
                t_relay();
                exit;
        }


Logs show:
Sep 26 15:29:08 kamailio /usr/sbin/kamailio[108044]: INFO: <script>: failure_route(ROUTEFAIL) @@ call to uac_auth()
Sep 26 15:29:08 kamailio /usr/sbin/kamailio[108044]: ERROR: tm [t_fwd.c:1723]: t_forward_nonack(): no branches for forwarding
Sep 26 15:29:08 kamailio /usr/sbin/kamailio[108044]: ERROR: tm [tm.c:1433]: _w_t_relay_to(): t_forward_noack failed

Here is the 401 received - to me, there is the challenge:

2017/09/26 15:32:16.410800  pro.vid.er.ip:5060 ->  my.kam.ailio.ip:5060
SIP/2.0 401 Unauthorized
Via: SIP/2.0/UDP  my.kam.ailio.ip;branch=z9hG4bK2edf.049073b8bcb252b5f7b5e6fffcd8b498.0;received= my.kam.ailio.ip;rport=5060
Via: SIP/2.0/UDP 46.105.145.36:5060;branch=z9hG4bK53167350
From: <sip:0600000000@46.105.145.36>;tag=as6fb1c402
To: <sip:100622222222@ my.kam.ailio.ip>;tag=as61ddd570
Call-ID: 242842785528c07b7fd56dc660b8c377@my.asterisk.ip:5060
CSeq: 102 INVITE
Server: OpenVoice-8
Allow: INVITE, ACK, CANCEL, OPTIONS, BYE, REFER, SUBSCRIBE, NOTIFY, INFO, PUBLISH
Supported: replaces
WWW-Authenticate: Digest algorithm=MD5, realm="sip8.voip-centrex.net", nonce="6b04a972"
Content-Length: 0





On Tue, Sep 26, 2017 at 9:27 AM, Daniel Tryba <d.tryba@pocos.nl> wrote:
On Tue, Sep 26, 2017 at 09:08:26AM -0400, Jean Cérien wrote:
> With the UACREG module, I am registering to a remote provider. Register
> goes out, 401 back, Register goes out with nonce & co, OK
>
> Later, when I send an invite, the provider issues an 401 Unauthorized. I
> guess it expects me to resubmit an INVITE with the authentication data, but
> I dont see how to do that.

Are you saying the 401 doesn't contain a challenge? Otherwise you
should just use uac_auth() (just like you probably already do for the
REGISTER), following URL contains an example for an INVITE:
https://www.kamailio.org/docs/modules/stable/modules/uac.html#uac.f.uac_auth


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