Min fætter kommer på besøg i weekenden, og min nevø vil gerne vise ham den nye cykel.

Because after a possessive like min, Danish normally uses the noun in its basic, indefinite form.

So you say:

• min fætter = my cousin
• min nevø = my nephew

not:

• min fætteren
• min nevøen

This is similar to English, where we say my cousin, not my the cousin.

A useful rule:

• possessive + noun → no definite ending on the noun

Examples:

• min bil = my car
• hendes søster = her sister
• vores hus = our house

Kommer på besøg is a very common Danish expression meaning comes to visit or is coming over.

So:

• Min fætter kommer på besøg = My cousin is coming to visit.

You could also use besøger, but it is a bit different in feel:

• Min fætter besøger mig = My cousin is visiting me.

The expression komme på besøg often sounds more natural in everyday speech when someone is coming over to see you.

Breakdown:

• kommer = comes / is coming
• på besøg = on a visit / to visit

So together it works like an idiom: come visit.

Even though it literally looks like in the weekend, the natural English meaning is at the weekend or on the weekend, depending on your variety of English.

In Danish, i weekenden is the normal expression for during the weekend / this coming weekend.

Examples:

• Vi ses i weekenden = We’ll see each other this weekend.
• Jeg arbejder i weekenden = I’m working this weekend.

So this is mainly something to memorize as a fixed time expression.

Vil gerne often means would like to or wants to, depending on context.

In this sentence:

• min nevø vil gerne vise ham den nye cykel

it means something like:

• my nephew would like to show him the new bike
• or my nephew wants to show him the new bike

Why both are possible:

• vil = will / wants to
• gerne adds the idea of willingness, pleasure, or desire

So vil gerne is softer and more natural than just vil in many situations.

Compare:

• Jeg vil spise = I want to eat / I will eat
• Jeg vil gerne spise = I’d like to eat

For learners, it is often best to think of vil gerne as would like to in many everyday sentences.

Because ham is the object form of the pronoun, while han is the subject form.

Here, the cousin is receiving the action of vise:

• min nevø vil gerne vise ham den nye cykel
• literally: my nephew would like to show him the new bike

So:

• han = he
• ham = him

Compare:

• Han kommer i weekenden = He is coming this weekend.
• Jeg kender ham = I know him.

This is very similar to English:

• he as subject
• him as object

Because in Danish, when you have both an indirect object and a direct object, a short pronoun like ham often comes before the thing being given, shown, sent, etc.

Here:

• ham = indirect object
• den nye cykel = direct object

So:

• vise ham den nye cykel = show him the new bike

This word order is very common in Danish.

Compare:

• Jeg gav hende en bog = I gave her a book.
• Han sendte mig en mail = He sent me an email.

You can also sometimes rephrase with a preposition:

• vise den nye cykel til ham = show the new bike to him

But in everyday Danish, vise ham den nye cykel is very natural.

This is an important Danish grammar pattern called double definiteness.

When a noun is definite and has an adjective before it, Danish usually uses:

• den/det/de + adjective + noun in indefinite form

So:

• den nye cykel = the new bike

not:

• den nye cyklen

Why? Normally, Danish often makes a noun definite by adding an ending:

• cykel = bike
• cyklen = the bike

But if there is an adjective, Danish usually switches to:

• den nye cykel

More examples:

• bilen = the car

• den røde bil = the red car

• huset = the house
• det store hus = the big house

So the pattern is:

• no adjective: cyklen
• with adjective: den nye cykel

Because the adjective is used in a definite phrase: den nye cykel.

In Danish, adjectives often change form depending on grammar. In a definite phrase, the adjective usually takes -e.

So:

• en ny cykel = a new bike
• den nye cykel = the new bike

Other examples:

• en stor bil = a big car

• den store bil = the big car

• et gammelt hus = an old house
• det gamle hus = the old house

So nye is the definite form of ny here.

Yes, it is normal main clause word order.

The second clause is:

• og min nevø vil gerne vise ham den nye cykel

In a regular Danish main clause, the usual order is:

• subject + verb + other elements

So here:

• min nevø = subject
• vil = finite verb
• gerne = adverb
• vise = infinitive
• ham den nye cykel = objects

This is standard word order.

A useful point: Danish often puts the finite verb in second position in main clauses. Here that works out naturally because the subject comes first:

• Min nevø | vil | gerne vise ham den nye cykel

If something else came first, then the subject would move after the verb:

• I weekenden vil min nevø gerne vise ham den nye cykel.

That is a very common Danish pattern.

Yes. Fætter specifically means a male cousin, while kusine means a female cousin.

So Danish makes a distinction that English usually does not:

• fætter = male cousin
• kusine = female cousin

English normally just says cousin unless the gender matters.

That means a native English speaker may need to get used to choosing between the two in Danish.

Because the sentence contains two full coordinated clauses:

1. Min fætter kommer på besøg i weekenden
2. og min nevø vil gerne vise ham den nye cykel

Each part has its own subject and verb:

• fætter kommer
• nevø vil

In Danish, commas are often used to separate clauses like this. Comma rules can vary depending on the comma system being followed, but a comma here is completely normal and helpful.

So the comma marks the boundary between two linked statements:

• my cousin is coming this weekend,
• and my nephew wants to show him the new bike.