the simplest infinite dimensional gelfand pairs are the ones of the form $(g,k) = \varinjlim (g_n,k_n)$ where the $(g_n,k_n)$ are finite dimensional gelfand pairs. here we take "gelfand pair" to mean that the action of $g$ on a suitable hilbert space $l^2(g/k)$ is multiplicity free, and we study several cases where that multiplicity free property holds. the strongest results are for cases where the $g_n$ are semidirect products $n_n\rtimes k_n$ with $n_n$ nilpotent. then the $n_n$ are commutative or $2$--step nilpotent. in many cases where the derived algebras $[\mathfrak{n}_n,\mathfrak{n}_n]$ are of bounded dimension we construct $g_n$--equivariant isometric maps $\zeta_n : l^2(g_n/k_n) \to l^2(g_{n+1}/k_{n+1})$ and prove that the left regular representation of $g$ on the hilbert space $l^2(g/k) := \varinjlim l^2(g_n/k_n),\zeta_n$ is a multiplicity free direct integral of irreducible unitary representations.