diff --git a/test/test_ea_mu_plus_lambda.py b/test/test_ea_mu_plus_lambda.py
index c9fd10d9..ab81c36b 100644
--- a/test/test_ea_mu_plus_lambda.py
+++ b/test/test_ea_mu_plus_lambda.py
@@ -69,6 +69,7 @@ def objective(ind):
         return ind
 
     population_params["n_parents"] = 1
+
     pop = cgp.Population(**population_params, genome_params=genome_params)
 
     ea = cgp.ea.MuPlusLambda(10, 10, 1)
@@ -125,3 +126,96 @@ def objective(ind):
 
     for idx in range(k_local_search, population_params["n_parents"]):
         assert pop[idx].genome._parameter_names_to_values["<p1>"] == pytest.approx(1.0)
+
+def test_n_offspring_less_than_n_breeding():
+    n_offsprings = 10
+    n_breedings = 5
+    with pytest.raises(ValueError):
+        _ = cgp.ea.MuPlusLambda(n_offsprings, n_breedings, 1)
+
+
+def test_fitness_wrong_return_type(population_params, genome_params):
+    def objective(individual):
+        individual.fitness = 5
+        return individual
+    
+    pop = cgp.Population(**population_params, genome_params=genome_params)
+    ea = cgp.ea.MuPlusLambda(10, 10, 1)
+    ea.initialize_fitness_parents(pop, objective)
+
+    with pytest.raises(ValueError):
+        ea.step(pop, objective)
+
+
+def test_fitness_initialization(population_params, genome_params):
+    def objective(individual):
+        individual.fitness = -1.0
+        return individual
+
+    pop = cgp.Population(**population_params, genome_params=genome_params)
+
+    ea = cgp.ea.MuPlusLambda(10, 10, 1)
+    ea.initialize_fitness_parents(pop, objective)
+    assert all([ind.fitness is not None for ind in pop.parents])
+
+
+def test_one_step(population_params, genome_params):
+    def objective(individual):
+        individual.fitness = float(individual.idx)
+        return individual
+
+    pop = cgp.Population(**population_params, genome_params=genome_params)
+    n_offsprings = 10
+    ea = cgp.ea.MuPlusLambda(n_offsprings, 10, 1)
+    ea.initialize_fitness_parents(pop, objective)
+    old_parent_ids = sorted([ind.idx for ind in pop.parents])
+    ea.step(pop, objective)
+    new_parent_ids = sorted([ind.idx for ind in pop.parents])
+    # After one step, the new parent population should have IDs that
+    # are offset from the old parent ids by n_offsprings
+    # This is by construction in this test because the fitness is equal to the id
+    assert all(
+        [new_id == old_id + n_offsprings for new_id, old_id in zip(new_parent_ids, old_parent_ids)]
+    )
+
+
+def test_fitness_sort(population_params, genome_params):
+    def objective(individual):
+        individual.fitness = float(individual.idx)
+        return individual
+
+    pop = cgp.Population(**population_params, genome_params=genome_params)
+    n_offsprings = 10
+    ea = cgp.ea.MuPlusLambda(n_offsprings, 10, 1)
+    ea.initialize_fitness_parents(pop, objective)
+    sorted_parents = ea._sort(pop.parents)
+    # Assert that the sorting inverted the list of parents (because the fitness is equal to the id)
+    assert sorted_parents == pop.parents[::-1]
+
+
+def test_create_new_populations(population_params, genome_params):
+    def objective(individual):
+        individual.fitness = float(individual.idx)
+        return individual
+
+    pop = cgp.Population(**population_params, genome_params=genome_params)
+    n_offsprings = 10
+    ea = cgp.ea.MuPlusLambda(n_offsprings, 10, 1)
+
+    ea.initialize_fitness_parents(pop, objective)
+
+    offsprings = ea._create_new_offspring_generation(pop)
+    assert len(offsprings) == n_offsprings
+    assert all([ind.idx >= pop.n_parents for ind in offsprings])
+    # Assert that all offspring dna are different from all parents dna
+    offspring_dna = [ind.genome.dna for ind in offsprings]
+    parent_dna = [ind.genome.dna for ind in pop.parents]
+    assert all([odna != pdna for odna in offspring_dna for pdna in parent_dna])
+
+    # Create new "parent" population from the offsprings and assert
+    # that we picked the 5 best ones (here, by construction, the 5
+    # highest ids)
+    offsprings = ea._compute_fitness(offsprings, objective)
+    offsprings = ea._sort(offsprings)
+    new_parents = ea._create_new_parent_population(pop.n_parents, offsprings)
+    assert [ind.idx for ind in new_parents] == [ind.idx for ind in offsprings[: pop.n_parents]]