Two years ago, I was three times as old as my brother. In three years, I will be twice as old as my brother. How old are we now?

To solve the problem, we need to set up a system of equations based on the information given. Let's define the variables:

- Let \( x \) be your current age.
- Let \( y \) be your brother's current age.

Step 1: Translate the first statement into an equation

The first statement says: "Two years ago, I was three times as old as my brother was."

- Two years ago, your age was \( x - 2 \).
- Two years ago, your brother's age was \( y - 2 \).

According to the statement:
\[
x - 2 = 3(y - 2)
\]

Expanding and simplifying:
\[
x - 2 = 3y - 6
\]
\[
x = 3y - 4 \quad \text{(Equation 1)}
\]

Step 2: Translate the second statement into an equation

The second statement says: "In three years, I will be twice as old as my brother."

- In three years, your age will be \( x + 3 \).
- In three years, your brother's age will be \( y + 3 \).

According to the statement:
\[
x + 3 = 2(y + 3)
\]

Expanding and simplifying:
\[
x + 3 = 2y + 6
\]
\[
x = 2y + 3 \quad \text{(Equation 2)}
\]

Step 3: Solve the system of equations

We now have two equations:
1. \( x = 3y - 4 \)
2. \( x = 2y + 3 \)

Since both expressions are equal to \( x \), we can set them equal to each other:
\[
3y - 4 = 2y + 3
\]

Solving for \( y \):
\[
3y - 2y = 3 + 4
\]
\[
y = 7
\]

Step 4: Find \( x \)

Substitute \( y = 7 \) back into Equation 1 (\( x = 3y - 4 \)):
\[
x = 3(7) - 4
\]
\[
x = 21 - 4
\]
\[
x = 17
\]

Step 5: Verify the solution

- Two years ago, your age was \( 17 - 2 = 15 \), and your brother's age was \( 7 - 2 = 5 \). Check if you were three times as old:
\[
15 = 3 \times 5 \quad \text{(True)}
\]

- In three years, your age will be \( 17 + 3 = 20 \), and your brother's age will be \( 7 + 3 = 10 \). Check if you will be twice as old:
\[
20 = 2 \times 10 \quad \text{(True)}
\]

Both conditions are satisfied, so the solution is correct.

Final Answer:

\[
\boxed{17 \text{ and } 7}
\]

You are currently 17 years old, and your brother is currently 7 years old.