Let ψ,τ,0, be an entire f（?）nction defined by a B-Dirichletian element {ψ,τ,0,}: （?）P,n,（σ+i,τ,0,） exp （-λ,n,s）, where s=σ+iτ, τ,0, is an arbitrary fixed real unmber, λ,n, is a sequence of strictly increasing positive numbers tending to infinity with n and P,n,（s）=（?） a,nj,s,j,（n=1, 2, …）, are complex polynomials. We associate., it with a Dirichlet series ψ（s）= （?）A,n,exp（-λ,n,s）. where A,n,=（?）. It is shown in this paper that the （p, q） order （R） or lower order of ψ,τ,0, is eaqual to that of ψ whenever σ（?）=-∞, β’=（?） sup（（m,n,）/（λ,n,））,<,∞ and L=limsup （（logn）/（λ,n,））,<,∞, where （?） denotes the abscissa of convergence of ψ and p≥q+2. A necessary and sufficient condition under which ψ,τ,0, is of regular growth is also given