Peter I is dead in 1710

Depending on how things progress, Alexei may NEED to remarry in mid-1720ies, if Tsarevna Natalia dies on schedule and he is left with a single heir to the throne (before that, Natalia can be viewed as spare if you squint).
OK. By that time he is in his 30s and a victorious monarch who already was married to a royalty. With Russia staying out of the binding international commitments, there probably would be a wide variety of possible matches.

Speaking of which, with the GNW over what could be Russian options in foreign politics?

Trade interests are more or less pushing toward a closer alliance with Britain but not necessarily all the way to the binding military affiliations.

The Ottomans remain a potential problem which mostly shapes Russian interests in the PLC (not letting a French candidate to taKe a throne) and forces alliance with Austria (in OTL since 1727) and a wish to prevent a pro-French candidate to take the PLC throne (hence involvement in a war of the Polish Succession). The whole thing with the Ottomans during that period is hinging upon the Crimean raids and Ottoman unwillingness/in capability to stop them. IIRC, in OTL in 1736 the Ottomans did not strongly objected against Russian “punishment” of the Khanate but capture of the Ottoman-held Ochakov was a different issue. So, if we take Ottoman behavior for granted, then the war is a matter of time and alliance with Austria is logical.

There are certain domestic things which could be done differently realistically to produce different results in a coming war with the Ottomans.
 
The Ottomans remain a potential problem which mostly shapes Russian interests in the PLC (not letting a French candidate to taKe a throne) and forces alliance with Austria (in OTL since 1727) and a wish to prevent a pro-French candidate to take the PLC throne (hence involvement in a war of the Polish Succession). The whole thing with the Ottomans during that period is hinging upon the Crimean raids and Ottoman unwillingness/in capability to stop them. IIRC, in OTL in 1736 the Ottomans did not strongly objected against Russian “punishment” of the Khanate but capture of the Ottoman-held Ochakov was a different issue. So, if we take Ottoman behavior for granted, then the war is a matter of time and alliance with Austria is logical.
Interesting thing is that if Kettlers survive TTL (which they are likely), the Russian objectives during War of Polish Succession may diverge from OTL - up to supporting half-Romanov young Kettler prince (ATL son of Anna Ioannovna and Frederick Wilhelm) as their own independent candidate for Polish throne instead of joint support of Augustus III (though this is unlikely).

A strategic alliance that may need to be secured ASAP for Baltic trade guarantees is Denmark, and I have the feeling that TTL Ekaterina Ioannovna match, if arranged, would be arranged in this direction.
 
Interesting thing is that if Kettlers survive TTL (which they are likely), the Russian objectives during War of Polish Succession may diverge from OTL - up to supporting half-Romanov young Kettler prince (ATL son of Anna Ioannovna and Frederick Wilhelm) as their own independent candidate for Polish throne instead of joint support of Augustus III (though this is unlikely).

A strategic alliance that may need to be secured ASAP for Baltic trade guarantees is Denmark, and I have the feeling that TTL Ekaterina Ioannovna match, if arranged, would be arranged in this direction.

Kettles candidacy is interesting because it could create 3 ways split instead of 2, each with its own support: Stanislavsky - France, August - Hapsburgs, Kettler - Russia. IIRC, in OTL Stas got more votes and it was an “alternative Sejm” that asked for the Russian intervention on August’s behalf. With 3 candidates Kettler could get traction as (a) being “almost Polish” and (b) not being associated with any negative feelings related to any of the OTL candidates. Not to mention that, France and Austria being at each other throats and having to settle scores elsewhere (and as a result not having too much military resource for open confrontation with Russia) both of them may consider him an acceptable compromise and the War of Polish Succession ends up with a different name because it is being fought anywhere but in Poland. OTOH, it is interesting how an issue of Lorraine would be resolved without Austrian candidate getting PLC throne (not sure if in OTL these two issues were resolved as a part of a “package”).

Of course, this may (or may not) negatively impact Russian-Austrian alliance but in OTL Austrian participation in the next Ottoman war was anything but helpful to Russia.

As far as Denmark is involved, IIRC, Russian-Danish relations had been quite friendly even if this was hardly relevant from trade perspective: practically all goods had been carried by the foreign ships, British and Dutch.
 
As far as Denmark is involved, IIRC, Russian-Danish relations had been quite friendly even if this was hardly relevant from trade perspective: practically all goods had been carried by the foreign ships, British and Dutch.
Nevertheless, it's the most important Baltic ally IMO (and the Russians have been looking for Danish marriage market since the times of Boris Godunov, if not before).
 
Of course, there's also the question (in Denmark) of Karl Friedrich of Holstein. He's heir to Sweden (until his uncle has a kid or his aunt pushes him out like OTL). So, Denmark will want to avoid such a personal union (Sweden-Holstein), or at least have an ally (Russia) against it should it come to pass.
Of course, Karl Friedrich is unlikely to wed Anna Petrovna here, and the Ivanovna girls are too old. Which opens up the question of where he might marry instead?
 
Of course, there's also the question (in Denmark) of Karl Friedrich of Holstein. He's heir to Sweden (until his uncle has a kid or his aunt pushes him out like OTL). So, Denmark will want to avoid such a personal union (Sweden-Holstein), or at least have an ally (Russia) against it should it come to pass.
Of course, Karl Friedrich is unlikely to wed Anna Petrovna here, and the Ivanovna girls are too old. Which opens up the question of where he might marry instead?

Denmark and Russia remained mostly on the good terms even with Russian Holstein marriage (AFAIK, only Peter III was planning a war with Denmark over Schleswig) so n absence of the matrimonial connection would hardly matter. Also, taking into an account that Russian trade had been done mostly by the British and Dutch ships, the issues of the Sund taxes was to be discussed with these parties. Russian navy in OTL had been happily rotting in the Gulf of Finland all the way to the 1st Archipelago Expedition of Catherine II so no conflict there either (and the only possible confrontation would be with Sweden).
 
Nevertheless, it's the most important Baltic ally IMO (and the Russians have been looking for Danish marriage market since the times of Boris Godunov, if not before).
Yes, they are an ally but don’t forget that during the GNW they were scared enough by Peter’s activities to ask him not to send troops to Stralsund and later to make a separate peace with Sweden. We can assume that less expansionist policy of Alexei eliminates these issues and that the relations remain friendly even without a marriage because there are no conflicting interests.
 
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