How to have two methods calling each other?

Solution 1:

'let rec... and...' is the syntax you seek.

let rec F() = 
    G()
and G() =
    F()

See also Adventures in F# Co-Recursion.

Solution 2:

Since the question is about methods, and Brian's answer is about functions, maybe it's useful to point out that you can use a similar syntax for types:

type A() =
    let b = new B()
    member x.MethodA() = b.MethodB()
and B() =
    member x.MethodB() = ()

Note also that members are 'let rec' by default (in fact I don't think they can be not recursive).