We prove that any complex differential equation with two monomials of the form z˙ = azk ¯zl + bzm¯zn, with k, l, m, n non-negative integers and a, b ∈ C, has one limit cycle at most. Moreover, we characterise when such a limit exists and prove that then it is hyperbolic. For an arbitrary equation of the above form, we also solve the centrefocus problem and examine the number, position, and type of its critical points. In particular, we prove a Berlinski˘ı-type result regarding the geometrical distribution of the critical points stabilities.