The appellants in this case, former asbestos workers, appeal from an order of the district court granting summary judgment to appellee A.C. and S., Inc. Because the appellants have failed to establish the existence of a genuine issue of material fact, we affirm.

A.C. and S. is a contracting company that has been engaged in the installation of thermal insulation materials since 1958. Some of the materials installed by A.C. and S.employees during that time have contained asbestos. Each of the appellants has worked as an insulator for several different contractors, including A.C. and S., at various construction sites in Nebraska. The appellants now claim that A.C. and S. negligently exposed them to asbestos, causing them to develop asbestos-related illnesses.

It is undisputed that the Nebraska Workers Compensation Act “provides the exclusive remedy by the employee against the employer for any injury arising out of and in the course of his employment.” P.A.M. v. Quad L. Associates, 221 Neb. 642, 645, 380 N.W.2d 243, 246 (1986). The appellants here do not contend, however, that A.C. and S. exposed them to asbestos during the course of their employment with A.C. and S. Rather, they claim that A.C. and S. negligently exposed them to asbestos while they were working for other contractors at work sites where A.C. and S. was installing asbestos-containing materials.

The district court granted summary judgment for A.C. and S. based on the appellants’ failure to show a genuine issue of material fact. According to the district court, the appellants relied upon “vague recollections by the deposed witnesses of probable job sites and probable simultaneous working times.” We review de novo a grant of summary judgment. Postscript Enterprises v. City of Bridgeton, 905 F.2d 223, 225 (8th Cir. 1990). Summary judgment is appropriate if “there is *132no genuine issue as to any material fact and ... the moving party is entitled to judgment as a matter of law.” Fed. R.Civ.P. 56(c). Upon moving for summary judgment, a party need only “point[ ] out to the district court ... that there is an absence of evidence to support the nonmoving party’s cause.” Celotex Corp. v. Catrett, 477 U.S. 317, 325, 106 S.Ct. 2548, 2554, 91 L.Ed.2d 265 (1986). The nonmoving party has the burden of showing that there is a “genuine issue of material fact” as to each essential element of that party’s case. Id. at 322-23, 106 S.Ct. at 2552.

In order to prevail at trial, the appellants would have to show that A.C. and S. exposed them to asbestos while they were employed by another contractor. The evidence offered by the appellants in response to A.C. and S.’s motion for summary judgment fails to create a genuine issue of material fact on this essential element of the appellants’ case. In a series of depositions and affidavits, the appellants state only that they worked at certain job sites; that A.C. and S. also had employees working at the same job sites; and that, in some cases, they believe that the A.C. and S. employees at those sites were working with asbestos. These depositions and affidavits contain no firm dates and no specific allegations that A.C. and S. employees exposed the appellants to asbestos.1 The deposition testimony of William Gilmore, a former A.C. and S. manager, is similarly vague.

The appellants might have avoided summary judgment had they been more specific in their allegations and presented some evidence that A.C. and S. exposed them to asbestos. It is not enough to state only that the appellants worked at certain job sites concurrently with A.C. and S. employees; some circumstantial or direct evidence of the appellants’ exposure to asbestos and of the nature and duration of such exposure would be necessary to establish a genuine issue of material fact. Accordingly, we affirm.