Given a planar system of nonautonomous ordinary differential equations, / = ( , ), conditions are given for the existence of an associative commutative unital algebra A with unit and a function : Ω ⊂ R 2 × R 2 → R 2 on an open set Ω such that ( , ) = ( , ) and the maps 1 ( ) = ( , ) and 2 ( ) = ( , ) are Lorch differentiable with respect to A for all ( , ) ∈ Ω, where and represent variables in A. Under these conditions the solutions ( ) of the differential equation / = ( , ) over A define solutions ( ( ), ( )) = ( ) of the planar system.