We obtain new existence and uniqueness theorems of pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations d d t [ u ( t ) + f ( t , u ( t ) ) ] = A ( t ) [ u ( t ) + f ( t , u ( t ) ) ] + g ( t , u ( t ) ) , t ∈ R , d d t [ u ( t ) + f ( t , B u ( t ) ) ] = A ( t ) [ u ( t ) + f ( t , B u ( t ) ) ] + g ( t , C u ( t ) ) , t ∈ R , assuming that A ( t ) satisfy “Acquistapace–Terreni” conditions, the evolution family generated by A ( t ) has exponential dichotomy, R ( λ 0 , A ( ⋅ ) ) is almost periodic, B , C are densely defined closed linear operators, f , g are Lipschitz with respect to the second argument uniformly in the first argument, f is pseudo almost periodic in the first argument, g is Stepanov-like pseudo almost periodic in the first argument for p > 1 and jointly continuous. To illustrate our abstract results, two examples are given.